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Molecular Modeling and
Dynamics

Modeling Metods, Molecular Dynamics,
Computational Models and Computer
Simulations of Molecular Systems

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Molecular modeling

Molecular Modeling Metods

Molecular modeling

1. REDIRECT Molecular modelling

Molecular modelling

Molecular modelling is a collective term that refers to
theoretical methods and computational techniques to
model or mimic the behaviour of molecules. The
techniques are used in the fields of computational
chemistry, computational biology and materials science
for studying molecular systems ranging from small
chemical systems to large biological molecules and
material assemblies. The simplest calculations can be
performed by hand, but inevitably computers are required
to perform molecular modelling of any reasonably sized
system. The common feature of molecular modelling
techniques is the atomistic level description of the
molecular systems; the lowest level of information is
individual atoms (or a small group of atoms). This is in
contrast to quantum chemistry (also known as electronic
structure calculations) where electrons are considered
explicitly. The benefit of molecular modelling is that it
reduces the complexity of the system, allowing many more
particles (atoms) to be considered during simulations.

Molecular mechanics is one aspect of molecular
modelling, as it is refers to the use of classical
mechanics/Newtonian mechanics to describe the physical
basis behind the models. Molecular models typically The backbone dihedral angles are

, ., , . , n i . n .• i n included in the molecular model of

describe atoms (nucleus and electrons collectively) as

a protein.

point charges with an associated mass. The interactions

between neighbouring atoms are described by spring-like

interactions (representing chemical bonds) and van der Waals forces. The Lennard-Jones

potential is commonly used to describe van der Waals forces. The electrostatic interactions

are computed based on Coulomb's law. Atoms are assigned

Molecular modelling

coordinates in Cartesian space or in internal
coordinates, and can also be assigned velocities in
dynamical simulations. The atomic velocities are related
to the temperature of the system, a macroscopic
quantity. The collective mathematical expression is
known as a potential function and is related to the
system internal energy (U), a thermodynamic quantity
equal to the sum of potential and kinetic energies.
Methods which minimize the potential energy are
known as energy minimization techniques (e.g.,
steepest descent and conjugate gradient), while
methods that model the behaviour of the system with
propagation of time are known as molecular dynamics.

,;.> k >*r'

Modelling of ionic liquid

E = E h

+ E a

J bonds "I - ^'angle ~T ^dihedral ~T ^non- bonded
f^'non— bonded ^electrostatic \ ^vanderWaals

This function, referred to as a potential function, computes the molecular potential energy
as a sum of energy terms that describe the deviation of bond lengths, bond angles and
torsion angles away from equilibrium values, plus terms for non-bonded pairs of atoms
describing van der Waals and electrostatic interactions. The set of parameters consisting of
equilibrium bond lengths, bond angles, partial charge values, force constants and van der
Waals parameters are collectively known as a force field. Different implementations of
molecular mechanics use slightly different mathematical expressions, and therefore,
different constants for the potential function. The common force fields in use today have
been developed by using high level quantum calculations and/or fitting to experimental
data. The technique known as energy minimization is used to find positions of zero gradient
for all atoms, in other words, a local energy minimum. Lower energy states are more stable
and are commonly investigated because of their role in chemical and biological processes. A
molecular dynamics simulation, on the other hand, computes the behaviour of a system as a
function of time. It involves solving Newton's laws of motion, principally the second law, F
= ma. Integration of Newton's laws of motion, using different integration algorithms, leads
to atomic trajectories in space and time. The force on an atom is defined as the negative
gradient of the potential energy function. The energy minimization technique is useful for
obtaining a static picture for comparing between states of similar systems, while molecular
dynamics provides information about the dynamic processes with the intrinsic inclusion of
temperature effects.

Molecules can be modelled either in vacuum or in the presence of a solvent such as water.
Simulations of systems in vacuum are referred to as gas-phase simulations, while those that
include the presence of solvent molecules are referred to as explicit solvent simulations. In
another type of simulation, the effect of solvent is estimated using an empirical
mathematical expression; these are known as implicit solvation simulations.

Molecular modelling methods are now routinely used to investigate the structure, dynamics
and thermodynamics of inorganic, biological, and polymeric systems. The types of biological
activity that have been investigated using molecular modelling include protein folding,
enzyme catalysis, protein stability, conformational changes associated with biomolecular
function, and molecular recognition of proteins, DNA, and membrane complexes.

Molecular modelling

Popular software for molecular modelling

Abalone

AMBER

ADF

Ascalaph Designer

BALLView

Biskit

BOSS

Cerius2

Chimera

CHARMM

Coot (program) for X-ray crystallography of biological molecules

COSMOS (software) [3]

CP2K

CPMD

Firefly

GAMESS (UK)

GAMESS (US)

GAUSSIAN

Ghemical

GROMACS

GROMOS

Insightll

LAMMPS

MacroModel

MarvinSpace

Materials Studio

MDynaMix

MMTK

MOE (software) [5]

Molecular Docking Server

Molsoft ICM [6]

MOPAC

NAMD

NOCH

Oscail X

PyMOL

Q-Chem

Sirius

SPARTAN (software) [7]

STR3DI32 [8]

Sybyl (software) [9]

MCCCS Towhee [10]

TURBOMOLE

ReaxFF

VMD

WHATIF [11]

Molecular modelling

• xeo [12]

• YASARA [13]

• Zodiac (software)'- ^

See also

Cheminformatics

Computational chemistry

Density functional theory programs.

Force field in Chemistry

Force field implementation

List of nucleic acid simulation software

List of protein structure prediction software

Molecular Design software

Molecular dynamics

Molecular graphics

Molecular mechanics

Molecular model

Molecular modelling on GPU

Molecule editor

Monte Carlo method

Quantum chemistry computer programs

Semi-empirical quantum chemistry method

Software for molecular mechanics modelling

Structural Bioinformatics

External links

• Center for Molecular Modeling at the National Institutes of Health (NIH) [15] (U.S.
Government Agency)

• Molecular Simulation [16] , details for the Molecular Simulation journal ISSN: 0892-7022

(print), 1029-0435 (online)

ri7i

• The eCheminfo Network and Community of Practice in Informatics and Modeling

References

• M. P. Allen, D.J. Tildesley, Computer simulation of liquids, 1989, Oxford University
Press, ISBN 0-19-855645-4.

• A. R. Leach, Molecular Modelling: Principles and Applications, 2001, ISBN 0-582-38210-6

• D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to
Applications, 1996, ISBN 0-12-267370-0

• D. C. Rapaport, The Art of Molecular Dynamics Simulation, 2004, ISBN 0-521-82586-7

• R. J. Sadus, Molecular Simulation of Fluids: Theory, Algorithms and Object-Orientation,
2002, ISBN 0-444-51082-6

• K.I.Ramachandran, G Deepa and Krishnan Namboori. P.K. Computational Chemistry and
Molecular Modeling Principles and Applications 2008[18] ISBN 978-3-540-77302-3
Springer-Verlag GmbH

Molecular modelling

Homepage

[I] Agile Molecule (http://www.agilemolecule.com/index.html)

[2] York Structural Biology Laboratory (http://www.ysbl.york.ac.uk/~emsley/coot/)

[3] COSMOS (http://www.cosmos-software.de/ceJntro.html) - Computer Simulation of Molecular Structures

[4] ChemAxon (http://www.chemaxon.com/product/mspace.html)

[5] MOE - Molecular Operating Environment, Chemical Computing Group (http://www.chemcomp.com/)

[6] Molsoft (http://www.molsoft.com/)

[7] Wavefunction, Inc. (http://www.wavefun.com/)

[8] Exorga, Inc. (http://www.exorga.com/)

[9] Tipos (http://www.tripos.com/sybyl/)

[10] MCCCS Towhee (http://towhee.sourceforge.net/) - Monte Carlo for Complex Chemical Systems

[II] CMBI (http://swift.cmbi.ru.nl/whatif/)
[12] xeo (http://sourceforge.net/projects/xeo)
[13] YASARA (http://www.yasara.org/)

[14] ZedeN (http://www.zeden.org)

[15] http://cmm.info.nih.gov/modeling/

[16] http://www.tandf.co.uk/journals/titles/08927022.asp

[17] http://www.echeminfo.com/

[18] http ://www. amrita. edu/cen/ccmm

Quantum chemistry

Quantum chemistry is a branch of theoretical chemistry, which applies quantum
mechanics and quantum field theory to address issues and problems in chemistry. The
description of the electronic behavior of atoms and molecules as pertaining to their
reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the
border between chemistry and physics, and significant contributions have been made by
scientists from both fields. It has a strong and active overlap with the field of atomic
physics and molecular physics, as well as physical chemistry.

Quantum chemistry mathematically describes the fundamental behavior of matter at the

n l
molecular scale. It is, in principle, possible to describe all chemical systems using this

theory. In practice, only the simplest chemical systems may realistically be investigated in

purely quantum mechanical terms, and approximations must be made for most practical

purposes (e.g., Hartree-Fock, post Hartree-Fock or Density functional theory, see

computational chemistry for more details). Hence a detailed understanding of quantum

mechanics is not necessary for most chemistry, as the important implications of the theory

(principally the orbital approximation) can be understood and applied in simpler terms.

In quantum mechanics the Hamiltonian, or the physical state, of a particle can be expressed
as the sum of two operators, one corresponding to kinetic energy and the other to potential
energy. The Hamiltonian in the Schrodinger wave equation used in quantum chemistry does
not contain terms for the spin of the electron.

Solutions of the Schrodinger equation for the hydrogen atom gives the form of the wave
function for atomic orbitals, and the relative energy of the various orbitals. The orbital
approximation can be used to understand the other atoms e.g. helium, lithium and carbon.

Quantum chemistry

History

The history of quantum chemistry essentially began with the 1838 discovery of cathode
rays by Michael Faraday, the 1859 statement of the black body radiation problem by Gustav
Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical
system could be discrete, and the 1900 quantum hypothesis by Max Planck that any energy
radiating atomic system can theoretically be divided into a number of discrete energy
elements e such that each of these energy elements is proportional to the frequency v with
which they each individually radiate energy, as defined by the following formula:

€ = flV

where h is a numerical value called Planck's Constant. Then, in 1905, to explain the
photoelectric effect (1839), i.e., that shining light on certain materials can function to eject
electrons from the material, Albert Einstein postulated, based on Planck's quantum
hypothesis, that light itself consists of individual quantum particles, which later came to be
called photons (1926). In the years to follow, this theoretical basis slowly began to be
applied to chemical structure, reactivity, and bonding.

Electronic structure

The first step in solving a quantum chemical problem is usually solving the Schrodinger
equation (or Dirac equation in relativistic quantum chemistry) with the electronic molecular
Hamiltonian. This is called determining the electronic structure of the molecule. It can be
said that the electronic structure of a molecule or crystal implies essentially its chemical
properties.

Wave model

The foundation of quantum mechanics and quantum chemistry is the wave model, in which
the atom is a small, dense, positively charged nucleus surrounded by electrons. Unlike the
earlier Bohr model of the atom, however, the wave model describes electrons as "clouds"
moving in orbitals, and their positions are represented by probability distributions rather
than discrete points. The strength of this model lies in its predictive power. Specifically, it
predicts the pattern of chemically similar elements found in the periodic table. The wave
model is so named because electrons exhibit properties (such as interference) traditionally
associated with waves. See wave-particle duality.

Valence bond

Although the mathematical basis of quantum chemistry had been laid by Schrodinger in

1926, it is generally accepted that the first true calculation in quantum chemistry was that
of the German physicists Walter Heitler and Fritz London on the hydrogen (H ) molecule in

1927. Heitler and London's method was extended by the American theoretical physicist
John C. Slater and the American theoretical chemist Linus Pauling to become the
Valence-Bond (VB) [or Heitler-London-Slater-Pauling (HLSP)] method. In this
method, attention is primarily devoted to the pairwise interactions between atoms, and this
method therefore correlates closely with classical chemists' drawings of bonds.

Quantum chemistry

Molecular orbital

An alternative approach was developed in 1929 by Friedrich Hund and Robert S. Mulliken,
in which electrons are described by mathematical functions delocalized over an entire
molecule. The Hund-Mulliken approach or molecular orbital (MO) method is less
intuitive to chemists, but has turned out capable of predicting spectroscopic properties
better than the VB method. This approach is the conceptional basis of the Hartree-Fock
method and further post Hartree-Fock methods.

Density functional theory

The Thomas-Fermi model was developed independently by Thomas and Fermi in 1927.
This was the first attempt to describe many-electron systems on the basis of electronic
density instead of wave functions, although it was not very successful in the treatment of
entire molecules. The method did provide the basis for what is now known as density
functional theory. Though this method is less developed than post Hartree-Fock methods,
its lower computational requirements allow it to tackle larger polyatomic molecules and
even macromolecules, which has made it the most used method in computational chemistry
at present.

Chemical dynamics

A further step can consist of solving the Schrodinger equation with the total molecular
Hamiltonian in order to study the motion of molecules. Direct solution of the Schrodinger
equation is called quantum molecular dynamics, within the semiclassical approximation
semiclassical molecular dynamics, and within the classical mechanics framework molecular
dynamics (MD). Statistical approaches, using for example Monte Carlo methods, are also
possible.

Adiabatic chemical dynamics

Main article: Adiabatic formalism or Born-Oppenheimer approximation

In adiabatic dynamics, interatomic interactions are represented by single scalar
potentials called potential energy surfaces. This is the Born-Oppenheimer approximation
introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry
were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into
the RRKM theory in 1952 by Marcus who took the transition state theory developed by
Eyring in 1935 into account. These methods enable simple estimates of unimolecular
reaction rates from a few characteristics of the potential surface.

Non-adiabatic chemical dynamics

Non-adiabatic dynamics consists of taking the interaction between several coupled
potential energy surface (corresponding to different electronic quantum states of the
molecule). The coupling terms are called vibronic couplings. The pioneering work in this
field was done by Stueckelberg, Landau, and Zener in the 1930s, in their work on what is
now known as the Landau-Zener transition. Their formula allows the transition probability
between two diabatic potential curves in the neighborhood of an avoided crossing to be
calculated.

Quantum chemistry

Quantum chemistry and quantum field theory

The application of quantum field theory (QFT) to chemical systems and theories has become
increasingly common in the modern physical sciences. One of the first and most
fundamentally explicit appearances of this is seen in the theory of the photomagneton. In
this system, plasmas, which are ubiquitous in both physics and chemistry, are studied in
order to determine the basic quantization of the underlying bosonic field. However,
quantum field theory is of interest in many fields of chemistry, including: nuclear chemistry,
astrochemistry, sonochemistry, and quantum hydrodynamics. Field theoretic methods have
also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical
pi-electron methods.

See also

Atomic physics

Computational chemistry

Condensed matter physics

International Academy of Quantum Molecular Science

Physical chemistry

Quantum chemistry computer programs

Quantum electrochemistry

QMC@Home

Theoretical physics

Further reading

• Pauling, L. (1954). General Chemistry. Dover Publications. ISBN 0-486-65622-5.

• Pauling, L., and Wilson, E. B. Introduction to Quantum Mechanics with Applications to
Chemistry (Dover Publications) ISBN 0-486-64871-0

• Atkins, P.W. Physical Chemistry (Oxford University Press) ISBN 0-19-879285-9

• McWeeny, R. Coulson's Valence (Oxford Science Publications) ISBN 0-19-855144-4

• Landau, L.D. and Lifshitz, E.M. Quantum Mechanics-.Non-relativistic Theory (Course of
Theoretical Physics vol.3) (Pergamon Press)

• Bernard Pullman and Alberte Pullman. 1963. Quantum Biochemistry., New York and
London: Academic Press.

• Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press,
2006. Considers the extent to which chemistry and especially the periodic system has
been reduced to quantum mechanics. ISBN 0-19-530573-6.

• Simon, Z. 1976. Quantum Biochemistry and Specific Interactions., Taylor & Francis;
ISBN-13: 978-0856260872 and ISBN 0-85-6260878 .

Quantum chemistry 10

References

[1] http://cmmxit.nih. gov/modeling/guide_documents/quantum_mechanics_document.html| "Quantum Chemistry".
The NIH Guide to Molecular Modeling. National Institutes of Health, http://cmm.cit.nih.gov/modeling/
guidedocuments/quantum^mechanicsdocument.html. Retrieved on 2007-09-08.

External links

• The Sherrill Group - Notes (http://vergil.chemistry.gatech.edu/notes/index.html)

• ChemViz Curriculum Support Resources (http://www.shodor.org/chemviz/)

• Early ideas in the history of quantum chemistry (http://www.
quantum-chemistry-history, com/)

Nobel lectures by quantum chemists

• Walter Kohn's Nobel lecture (http://nobelprize.org/chemistry/laureates/1998/
kohn-lecture.html)

• Rudolph Marcus' Nobel lecture (http://nobelprize.org/chemistry/laureates/1992/
marcus-lecture . html)

• Robert Mulliken's Nobel lecture (http://nobelprize.org/chemistry/laureates/1966/
mulliken-lecture.html)

• Linus Pauling's Nobel lecture (http://nobelprize.org/chemistry/laureates/1954/
pauling-lecture.html)

• John Pople's Nobel lecture (http://nobelprize.org/chemistry/laureates/1998/
pople-lecture.html)

Molecular orbital theory

In chemistry, molecular orbital theory (MO theory) is a method for determining
molecular structure in which electrons are not assigned to individual bonds between atoms,
but are treated as moving under the influence of the nuclei in the whole molecule. In this
theory, each molecule has a set of molecular orbitals, in which it is assumed that the
molecular orbital wave function \y may be written as a simple weighted sum of the n
constituent atomic orbitals j., according to the following equation: 1 '

1=1

The c coefficients may be determined numerically by substitution of this equation into the
Schrodinger equation and application of the variational principle. This method is called the
linear combination of atomic orbitals approximation and is used in computational
chemistry. An additional unitary transformation can be applied on the system to accelerate
the convergence in some computational schemes. Molecular orbital theory was seen as a
competitor to valence bond theory in the 1930s, before it was realized that the two methods
are closely related and that when extended they become equivalent.

Molecular orbital theory 1 \

History

Molecular orbital theory was developed, in the years after valence bond theory (1927) had
been established, primarily through the efforts of Friedrich Hund, Robert Mulliken, John C.
Slater, and John Lennard -Jones. MO theory was originally called the Hund-Mulliken
theory. The word orbital was introduced by Mulliken in 1932. By 1933, the molecular
orbital theory had become accepted as a valid and useful theory. According to German
physicist and physical chemist Erich Hiickel, the first quantitative use of molecular orbital
theory was the 1929 paper of Lennard -Jones. The first accurate calculation of a molecular
orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen
molecule. By 1950, molecular orbitals were completely defined as eigenfunctions (wave
functions) of the self-consistent field Hamiltonian and it was at this point that molecular
orbital theory became fully rigorous and consistent. This rigorous approach is known as
the Hartree-Fock method for molecules although it had its origins in calculations on atoms.
In calculations on molecules, the molecular orbitals are expanded in terms of an atomic
orbital basis set, leading to the Roothaan equations. This led to the development of many
ab initio quantum chemistry methods. Parallel to this rigorous development, molecular
orbital theory was applied in an approximate manner using some empirically derived
parameters in methods now known as semi-empirical quantum chemistry methods.

Overview

Molecular orbital (MO) theory uses a linear combination of atomic orbitals to form
molecular orbitals which cover the whole molecule. These are often divided into bonding
orbitals, anti-bonding orbitals, and non-bonding orbitals. A molecular orbital is merely a
Schrodinger orbital which includes several, but often only two nuclei. If this orbital is of
type in which the electron(s) in the orbital have a higher probability of being between
nuclei than elsewhere, the orbital will be a bonding orbital, and will tend to hold the nuclei
together. If the electrons tend to be present in a molecular orbital in which they spend
more time elsewhere than between the nuclei, the orbital will function as an anti-bonding
orbital and will actually weaken the bond. Electrons in non-bonding orbitals tend to be in
deep orbitals (nearly atomic orbitals) associated almost entirely with one nucleus or the
other, and thus they spend equal time between nuclei or not. These electrons neither
contribute nor detract from bond strength.

Molecular orbitals are further divided according to the types of atomic orbitals combining
to form a bond. These orbitals are results of electron-nucleus interactions that are caused
by the fundamental force of electromagnetism. Chemical substances will form a bond if
their orbitals become lower in energy when they interact with each other. Different
chemical bonds are distinguished that differ by electron cloud shape and by energy levels.

MO theory provides a global, delocalized perspective on chemical bonding. For example, in
the MO theory for hypervalent molecules it is unnecessary to invoke a major role for
d-orbitals, whereas valence bond theory normally uses hybridization with d-orbitals to
explain hypervalency. In MO theory, any electron in a molecule may be found anywhere in
the molecule, since quantum conditions allow electrons to travel under the influence of an
arbitrarily large number of nuclei, so long as permitted by certain quantum rules. Although
in MO theory some molecular orbitals may hold electrons which are more localized between
specific pairs of molecular atoms, other orbitals may hold electrons which are spread more
uniformly over the molecule. Thus, overall, bonding (and electrons) are far more delocalized

Molecular orbital theory

(spread out) in MO theory, than is implied in valence bond (VB) theory. This makes MO
theory more useful for the description of extended systems.

An example is that in the MO picture of benzene, composed of a hexagonal ring of 6 carbon
atoms. In this molecule, 24 of the 30 total valence bonding electrons are located in 12 o
(sigma) bonding orbitals which are mostly located between pairs of atoms (C-C or C-H),
similar to the valence bond picture. However, in benzene the remaining 6 bonding electrons
are located in 3 n (pi) molecular bonding orbitals that are delocalized around the ring. Two
are in an MO which has equal contributions from all 6 atoms. The other two orbitals have
vertical nodes at right angles to each other. As in the VB theory, all of these 6 delocalized pi
electrons reside in a larger space which exists above and below the ring plane. All
carbon-carbon bonds in benzene are chemically equivalent. In MO theory this is a direct
consequence of the fact that the 3 molecular pi orbitals form a combination which evenly
spreads the extra 6 electrons over 6 carbon atoms.

In molecules such as methane, the 8 valence electrons are found in 4 MOs that are spread
out over all 5 atoms. However, it is possible to approximate the MOs with 4 localized
orbitals similar in shape to sp hybrid orbitals predicted by VB theory. This is often
adequate for o (sigma) bonds, but it is not possible for the n (pi) orbitals. However, the
delocalized MO picture is more appropriate for ionization and spectroscopic predictions.
Upon ionization of methane, a single electron is taken from the MO which surrounds the
whole molecule, weakening all 4 bonds equally. VB theory would predict that one electron
is removed for an sp orbital, resulting in the need for resonance between four valence
bond structures, each of which has a one-electron bond.

As in benzene, in substances such as beta carotene, chlorophyll or heme, some electrons
the n (pi) orbitals are spread out in molecular orbitals over long distances in a molecule,
giving rise to light absorption in lower energies (visible colors), a fact which is observed.
This and other spectroscopic data for molecules are better explained in MO theory, with an
emphasis on electronic states associated with multicenter orbitals, including mixing of
orbitals premised on principles of orbital symmetry matching. The same MO principles also
more naturally explain some electrical phenomena, such as high electrical conductivity in
the planar direction of the hexagonal atomic sheets that exist in graphite. In MO theory,
"resonance" (a mixing and blending of VB bond states) is a natural consequence of
symmetry. For example, in graphite, as in benzene, it is not necessary to invoke the sp
hybridization and resonance of VB theory, in order to explain electrical conduction. Instead,
MO theory simply recognizes that some electrons in the graphite atomic sheets are
completely delocalized over arbitrary distances, and reside in very large molecular orbitals
that cover an entire graphite sheet, and some electrons are thus as free to move and
conduct electricity in the sheet plane, as if they resided in a metal.

See also

• Ab initio quantum chemistry methods

• Atomic orbital

• Configuration interaction

• Coupled cluster

• Hartree-Fock

• Molecular orbital

• MO diagram

• Moller-Plesset perturbation theory

• Quantum chemistry computer programs

• Semi-empirical quantum chemistry methods

Molecular orbital theory 13

References

[I] Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. ISBN 0-19-860918-3.
[2] Licker, Mark, J. (2004). McGraw-Hill Concise Encyclopedia of Chemistry. New York: McGraw-Hill. ISBN

0-07-143953-6.
[3] Coulson, Charles, A. (1952). Valence. Oxford at the Clarendon Press.
[4] Spectroscopy, Molecular Orbitals, and Chemical Bonding (http://nobelprize.org/nobel_prizes/chemistry/

laureates/1966/mulliken-lecture.pdf) - Robert Mulliken's 1966 Nobel Lecture
[5] Lennard-Jones Paper of 1929 (http://www.guantum-chemistry-history.com/LeJo_Dat/LJ-Halll.htm) -

Foundations of Molecular Orbital Theory.
[6] Hiickel, E. (1934). Trans. Faraday Soc. 30, 59.
[7] Coulson, C.A. (1938). Proc. Camb. Phil. Soc. 34, 204.
[8] Hall, G.G. Lennard-Jones, Sir John. (1950). Proc. Roy. Soc.A202, 155.
[9] Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 65 - 69, ISBN 471

98055
[10] Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pg 81 - 92, ISBN 471

98055

[II] Introduction to Molecular Orbital Theory (http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.
html) - Imperial College London

External links

• Molecular Orbital Theory (http://chemed.chem.purdue.edu/genchem/topicreview/bp/
ch8/mo.html) - Purdue University

• Molecular Orbital Theory (http://www.sparknotes.com/chemistry/bonding/
molecularorbital/sectionl.html) - Sparknotes

• Molecular Orbital Theory (http://www.mpcfaculty.net/mark_bishop/
molecular_orbital_theory.htm) - Mark Bishop's Chemistry Site

• Introduction to MO Theory (http://www.chem.qmul.ac.uk/software/download/mo/) -
Queen Mary, London University

• Molecular Orbital Theory (http://www.chm.davidson.edu/ChemistryApplets/
MolecularOrbitals/index.html) - a related terms table

Linear combination of atomic orbitals molecular orbital method 14

Linear combination of atomic orbitals
molecular orbital method

Electronic structure methods

Tight binding

Nearly-free electron model

Hartree-Fock

Modern valence bond

Generalized valence bond

Moller-Plesset perturbation theory

Configuration interaction

Coupled cluster

Multi-configurational self-consistent field

Density functional theory

Quantum chemistry composite methods

Quantum Monte Carlo

kp perturbation theory

Muffin-tin approximation

LCAO method

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic
orbitals and a technique for calculatinq molecular orbitals in quantum chemistry. In
quantum mechanics, electron confiqurations of atoms are described as wavefunctions. In
mathematical sense, these wave functions are the basis set of functions, the basis functions,
which describe the electrons of a qiven atom. In chemical reactions, orbital wavefunctions
are modified, i.e. the electron cloud shape is chanqed, accordinq to the type of atoms
participatinq in the chemical bond.

It was introduced in 1929 by Sir John Lennard-Jones with the description of bondinq in the
diatomic molecules of the first main row of the periodic table, but had been used earlier by
Linus Paulinq for H 2 + . [2] [3]

A mathematical description is

& = CiXl + C 2X2 + csXs H r c„x„

where 0i (phi) is a molecular orbital represented as the sum of n atomic orbitals Xr(chi),
each multiplied by a correspondinq coefficient c r . The coefficients are the weiqhts of the
contributions of the n atomic orbitals to the molecular orbital. The Hartree-Fock procedure
is used to obtain the coefficients of the expansion from the Hartree-Fock procedure.
The orbitals are thus expressed as linear combinations of basis functions, and the basis
functions are one-electron functions centered on nuclei of the component atoms of the
molecule. The atomic orbitals used are typically those of hydroqen-like atoms since these

Linear combination of atomic orbitals molecular orbital method

are known analytically i.e. Slater-type orbitals but other choices are possible like Gaussian
functions from standard basis sets.

By minimizing the total energy of the system, an appropriate set of coefficients of the linear
combinations is determined. This quantitative approach is now known as the Hartree-Fock
method. However, since the development of computational chemistry, the LCAO method
often refers not to an actual optimization of the wave function but to a qualitative
discussion which is very useful for predicting and rationalizing results obtained via more
modern methods. In this case, the shape of the molecular orbitals and their respective
energies are deduced approximately from comparing the energies of the atomic orbitals of
the individual atoms (or molecular fragments) and applying some recipes known as level
repulsion and the like. The graphs that are plotted to make this discussion clearer are
called correlation diagrams. The required atomic orbital energies can come from
calculations or directly from experiment via Koopmans' theorem.

This is done by using the symmetry of the molecules and orbitals involved in bonding. The
first step in this process is assigning a point group to the molecule. A common example is
water, which is of C symmetry. Then a reducible representation of the bonding is
determined demonstrated below for water:

C: v

E C2 a v (xz) a v '(yz)

ro = A) +■ B 2

Each operation in the point group is performed upon the molecule. The number of bonds
that are unmoved is the character of that operation. This reducible representation is
decomposed into the sum of irreducible representations. These irreducible representations
correspond to the symmetry of the orbitals involved.

MO diagrams provide simple qualitative LCAO treatment.

**■

Quantitative theories are the Huckel method, the extended Huckel method and the
Pariser-Parr-Pople method.

Linear combination of atomic orbitals molecular orbital method 16

See also

• Quantum chemistry computer programs

• Hartree-Fock

• Basis set (chemistry)

• Tight binding

External links

• LCAO @ chemistry.umeche.maine.edu Link [ ]

References

[1] Huheey, James. Inorganic Chemistry.Principles of Structure and Reactivity

[2] Friedrich Hund and Chemistry, Werner Kutzelnigg, on the occasion of Hund's 100th birthday, Angewandte

Chemie, 35, 573 - 586, (1996)
[3] Robert S. Mulliken's Nobel Lecture, Science, 157, no. 3785, 13 - 24, (1967)
[4] http://chemistry.umeche.maine.edu/Modeling/lcao.html

Hiickel method

The Hiickel method or Hiickel molecular orbital method (HMO) proposed by Erich
Hiickel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals

(LCAO MO) method for the determination of energies of molecular orbitals of pi electrons in

rn r2i
conjugated hydrocarbon systems, such as ethene, benzene and butadiene. It is the

theoretical basis for the Hiickel's rule; the extended Hiickel method developed by Roald

T31

Hoffmann is the basis of the Woodward-Hoffmann rules .It was later extended to
conjugated molecules such as pyridine, pyrrole and furan that contain atoms other than
carbon, known in this context as heteroatoms.

It is a very powerful educational tool and details appear in many chemistry textbooks.

Hiickel characteristics

The method has several characteristics:

• It limits itself to conjugated hydrocarbons

• Only pi electron MO's are included because these determine the general properties of
these molecules and the sigma electrons are ignored. This is referred to as sigma-pi
separability.

• The method takes as inputs the LCAO MO Method, the Schrodinger equation and
simplifications based on orbital symmetry considerations. Interestingly the method does
not take in any physical constants.

• The method predicts how many energy levels exist for a given molecule, which levels are
degenerate and it expresses the MO energies as the sum of two other energy terms
called alpha, the energy of an electron in a 2p-orbital and beta, an interaction energy
between two p orbitals which are still unknown but importantly have become
independent of the molecule. In addition it enables calculation of charge density for each
atom in the pi framework, the bond order between any two atoms and the overall
molecular dipole moment.

Hiickel method

Hiickel results

The results for a few simple molecules are tabulated below:

Molecule

Energy

Frontier orbital

HOMO
gap

LUMO energy

Ethylene

Ej-a-P

LUMO

-2p

E 2 = a + p

HOMO

Butadiene

E = a + 1.62P

E 2 = a + 0.62P

HOMO

-1.24P

E 3 = a-0.62p

LUMO

E 4 = a- 1.62P

Benzene

E = a + 2P

E 2 = a + p

E 3 =a + p

HOMO

-2p

E 4 = « - P

LUMO

E 5 =a-p

E 6 =a-2p

Cyclobutadiene

E = a + 2P

E 2 =a

SOMO

E 3 = a

SOMO

E 4 =a-2p

Table 1 . Hiickel method results L

owest energies op top a an(

[5]
I p are both negative values

The theory predicts two energy levels for ethylene with its two pi electrons filling the
low-energy HOMO and the high energy LUMO remaining empty. In butadiene the 4 pi
electrons occupy 2 low energy MO's out of a total of 4 and for benzene 6 energy levels are
predicted two of them degenerate.

For linear and cyclic systems (with n atoms), general solutions exist .

_ _ kn

Linear: E k = a + 28 cos

Cyclic: Ejt = Of + 2/3 cos

(fi + 1)
2for

Many predictions have been experimentally verified:

• The HOMO - LUMO gap in terms of the |3 constant correlates directly with the respective
molecular electronic transitions observed with UV/VIS spectroscopy. For linear polyenes
the energy gap is given as:

-A3 sin

2(71 + 1)

from which a value for |3 can be obtained between -60 and -70 kcal/mol (-250 to
-290 kJ/mol). [7]

• The predicted MO energies as stipulated by Koopmans' theorem correlate with

photoelectron spectroscopy.

[8]

Hiickel method 18

• The Hiickel derealization energy correlates with the experimental heat of combustion.
This energy is defined as the difference between the total predicted pi energy (in
benzene 8B) and a hypothetical pi energy in which all ethylene units are assumed isolated
each contributing 2 (3 (making benzene 3 x 2 (3 = 6B).

• Molecules with MO's paired up such that only the sign differs (for example a+/-|3) are
called alternant hydrocarbons and have in common small molecular dipole moments.
This is in contrast to non-alternant hydrocarbons such as azulene and fulvene that have
large dipole moments. The Hiickel-theory is more accurate for alternant hydrocarbons.

• For cyclobutadiene the theory predicts that the two high-energy electrons occupy a
degenerate pair of MO's that are neither stabilized or destabilized. Hence the square
molecule would be a very reactive triplet diradical (the ground state is actually
rectangular without degenerate orbitals). In fact, all cyclic conjugated hydrocarbons with
a total of An pi electrons share this MO pattern and this form the basis of Huckel's rule.

Mathematics behind the Hiickel method

The Hiickel method can be derived from the Ritz method with a few further assumptions
concerning the overlap matrix S and the Hamiltonian matrix H.

It is assumed that the overlap matrix S is the identity matrix. This means that overlap
between the orbitals is neglected and the orbitals are considered orthogonal. Then the
generalised eigenvalue problem of the Ritz method turns into an eigenvalue problem.

The Hamiltonian matrix H = (H ..) is parametrised in the following way:

H.. = a for C atoms and a + h A B for other atoms A.

ii A K

H.. = (3 if the two atoms are next to each other and both C, and k B for other neighbouring
atoms A and B.

H.. = in any other case

The orbitals are the eigenvectors and the energies are the eigenvalues of the Hamiltonian
matrix. If the substance is a pure hydrocarbon the problem can be solved without any
knowledge about the parameters. For heteroatom systems, such as pyridine, values of h

and k have to be specified.

Hiickel solution for ethylene

In the Hiickel treatment for ethylene , the molecular orbital \I'is a linear combination of
the 2p atomic orbitals at carbon with their ratio's c :

This equation is substituted in the Schrodinger equation:

m> = E$

with H the Hamiltonian and E the energy corresponding to the molecular orbital
to give:

i?ci0! + Hc 2 <fe = Ecifa + Eczfo

This equation is multiplied by 0iand integrated to give the equation:

Cl (H u - ES n ) + c 2 (H 12 - ES 12 ) =
The same equation is multiplied by 0-zand integrated to give the equation:
Cl (H 21 - ES 12 ) + c 2 {H 22 - ES 22 ) =

Hiickel method

where:

All diagonal Hamiltonian integrals Ha are called coulomb integrals and those of type Hij
, where atoms i and j are connected, are called resonance integrals with these
relationships:

H[[ = H-2-2 = Q

i?ia = H<n = 3
Other assumptions are that the overlap integral between the two atomic orbitals is

s±i = S22 = i
s 12 = o

leading to these two homogeneous eguations:

Cl {a - E) + c 2 j5 = Q

ci/3 + c 2 {a - E) = Q
with a total of five variables. After converting this set to matrix notation:

a — E

the trivial solution gives both wavefunction coefficients c equal to zero which is not useful
so the other (non-trivial) solution is :

a-E &

i3 a- ;:

which can be solved by expanding its determinant:

v2 o2

and

(a - Ef = ,3 2

a-E = ±3

E = a±3

After normalization the coefficients are obtained:

c-i =c 2

71'

The constant |3 in the energy term is negative and therefore a + |3 is the lower energy
corresponding to the HOMO and is a - |3 the LUMO energy.

Hiickel method 20

External links

• Hiickel method @ chem.swin.edu.au Link L '

Further reading

• The HMO-Model and its applications: Basis and Manipulation, E. Heilbronner and H.
Bock, English translation, 1976, Verlag Chemie.

• The HMO-Model and its applications: Problems with Solutions, E. Heilbronner and H.
Bock, English translation, 1976, Verlag Chemie.

• The HMO-Model and its applications: Tables of Hiickel Molecular Orbitals , E.
Heilbronner and H. Bock, English translation, 1976, Verlag Chemie.

References

[1] E. Hiickel, Zeitschrift fur Physik, 70, 204, (1931); 72, 310, (1931); 76, 628 (1932); 83, 632, (1933)

[2] Hiickel Theory for Organic Chemists, C. A. Coulson, B. O'Leary and R. B. Mallion, Academic Press,1978.

[3] Stereochemistry of Electrocyclic Reactions R. B. Woodward, Roald Hoffmann J. Am. Chem. Soc.; 1965; 87(2);

395-397. doi: 10.1021/ja01080a054 (http://dx.doi.org/10.1021/ja01080a054)
[4] Andrew Streitwieser, Molecular Orbital Theory for Organic Chemists, Wiley, New York, (1961)
[5] The chemical bond 2nd Ed. J.N. Murrel, S.F.A. Kettle, J.M. Tedder ISBN 0471907600)
[6] Quantum Mechanics for Organic Chemists. Zimmerman, H., Academic Press, New York, 1975.
[7] Use ofHuckel Molecular Orbital Theory in Interpreting the Visible Spectra of Polymethine Dyes: An

Undergraduate Physical Chemistry Experiment. Bahnick, Donald A. J. Chem. Educ. 1994, 71, 171.
[8] Huckel theory and photoelectron spectroscopy, von Nagy-Felsobuki, Ellak I.J. Chem. Educ. 1989, 66, 821.
[9] Quantum chemistry workbook Jean-Louis Calais ISBN 0471594350
[ 1 0] http ://www. chem. swin. edu. au/modules/mod3/huckel.html

Extended Huckel method

The extended Huckel method is a semiempirical quantum chemistry method, developed
by Roald Hoffmann since 1963. It is based on the Huckel method but, while the original
Huckel method only considers pi orbitals, the extended method also includes the sigma
orbitals.

The extended Huckel method can be used for determining the molecular orbitals, but it is
not very successful in determining the structural geometry of an organic molecule. It can
however determine the relative energy of different geometrical configurations. It involves
calculations of the electronic interactions in a rather simple way where the
electron-electron repulsions are not explicitly included and the total energy is just a sum of
terms for each electron in the molecule. The off-diagonal Hamiltonian matrix elements are
given by an approximation due to Wolfsberg and Helmholz that relates them to the diagonal
elements and the overlap matrix element.

H. = KS..(H. + H..)/2

y y ii jj

K is the Wolfsberg-Helmholtz constant, and is usually given a value of 1.75. In the extended
Huckel method, only valence electrons are considered; the core electron energies and
functions are supposed to be more or less constant between atoms of the same type. The
method uses a series of parametrized energies calculated from atomic ionization potentials
or theoretical methods to fill the diagonal of the Fock matrix. After filling the non-diagonal
elements and diagonalizing the resulting Fock matrix, the energies (eigenvalues) and
wavefunctions (eigenvectors) of the valence orbitals are found.

Extended Huckel method 21

It is common in many theoretical studies to use the extended Huckel molecular orbitals as a
preliminary step to determining the molecular orbitals by a more sophisticated method
such as the CNDO/2 method and ab initio quantum chemistry methods. Since the EHT basis
set is fixed, the monoparticle calculated wavefunctions must be projected to the basis set
where the accurate calculation is to be done. One usually does this by adjusting the orbitals
in the new basis to the old ones by least squares method. As only valence electron
wavefunctions are found by this method, one must fill the core electron functions by
orthonormalizing the rest of the basis set with the calculated orbitals and then selecting the
ones with less energy. This leads to the determination of more accurate structures and
electronic properties, or in the case of ab initio methods, to somewhat faster convergence.

The method was first used by Roald Hoffmann who developed, with Robert Burns
Woodward, rules for elucidating reaction mechanisms (the Woodward-Hoffmann rules). He
used pictures of the molecular orbitals from extended Huckel theory to work out the orbital
interactions in these cycloaddition reactions.

A closely similar method was used earlier by Hoffmann and William Lipscomb for studies of
boron hydrides. The off-diagonal Hamiltonian matrix elements were given as

proportional to the overlap integral.

H. = KS...

y y

This simplification of the Wolfsberg and Helmholz approximation is reasonable for boron
hydrides as the diagonal elements are reasonably similar due to the small difference in
electronegativity between boron and hydrogen.

The method works poorly for molecules that contain atoms of very different
electronegativity. To overcome this weakness, several groups have suggested iterative
schemes that depend on the atomic charge. One such method, that is still widely used in
inorganic and organometallic chemistry is the Fenske-Hall method.

A recent program for the extended Huckel method is YAeHMOP which stands for "yet
another extended Huckel molecular orbital package".

References

[1] Hoffmann, R. An Extended Huckel Theory. I. Hydrocarbons. J. Chem. Phys 1963, 39, 1397-1412. doi:

10.1063/1.1734456 (http://dx.doi.Org/10.1063/l.1734456)
[2] M. Wolfsberg and L.J. Helmholz Journal of Chemical Physics, 20, 837, (1952) doi: 10.1063/1.1700580 (http://

dx.doi.org/10. 1063/1. 1700580)
[3] R. Hoffmann and W. N. Lipscomb, Journal of Chemical Physics, 36, 2179, (1962) doi: 10.1063/1.1732849

(http://dx.doi.org/10. 1063/1. 1732849);37, 2872, (1962) doi: 10.1063/1.1733113 (http://dx.doi.org/10.

1063/1.1733113)
[4] W. N. Lipscomb Boron Hydrides, W. A. Benjamin Inc., New York, 1963, Chaper 3
[5] Hall, M. B. and Fenske, R. F., Inorganic Chemistry, 11, 768 (1972)
[6] jimp2 program (http://www.chem.tamu.edu/jimp2)
[7] Computational Chemistry, David Young, Wiley-Interscience, 2001. Appendix A. A.3.3 pg 343, YAeHMOP

Extended Huckel method

See also

• Erich Huckel

• Roald Hoffmann

Molecular graphics

Molecular graphics (MG) is the discipline and philosophy of studying molecules and their

properties through graphical representation. 1 J IUPAC limits the definition to
representations on a "graphical display device". Ever since Dalton's atoms and Kekule's
benzene, there has been a rich history of hand-drawn atoms and molecules, and these
representations have had an important influence on modern molecular graphics. This
article concentrates on the use of computers to create molecular graphics. Note, however,
that many molecular graphics programs and systems have close coupling between the
graphics and editing commands or calculations such as in molecular modelling.

Relation to molecular models

There has been a long tradition of creating
molecular models from physical materials.
Perhaps the best known is Crick and
Watson's model of DNA built from rods and
planar sheets, but the most widely used
approach is to represent all atoms and
bonds explicitly using the "ball and stick"
approach. This can demonstrate a wide
range of properties, such as shape, relative
size, and flexibility. Many chemistry
courses expect that students will have
access to ball and stick models. One goal of
mainstream molecular graphics has been to
represent the "ball and stick" model as
realistically as possible and to couple this
with calculations of molecular properties.

Figure 1 shows a small molecule (NH 3 CH 2 CH 2 C(OH)(P0 3 H)(P0 3 H)-), as drawn by the Jmol
program. It is important to realise that the colours are purely a convention. Molecules can
never be visible under any light microscope and atoms are not coloured, do not have hard
surfaces and do not reflect light. Bonds are not rod-shaped. If physical molecular models
had not existed, it is unlikely that molecular graphics would currently use this metaphor.

Fig. 1. Key: Hydrogen = white, carbon = grey,

nitrogen = blue, oxygen = red, and phosphorus :

orange.

Comparison of physical models with molecular graphics

Physical models and computer models have partially complementary strengths and
weaknesses. Physical models can be used by those without access to a computer and now
can be made cheaply out of plastic materials. Their tactile and visual aspects cannot be
easily reproduced by computers (although haptic devices have occasionally been built). On
a computer screen, the flexibility of molecules is also difficult to appreciate; illustrating the

Molecular graphics 23

pseudorotation of cyclohexane is a good example of the value of mechanical models.

However, it is difficult to build large physical molecules, and all-atom physical models of
even simple proteins could take weeks or months to build. Moreover, physical models are
not robust and they decay over time. Molecular graphics is particularly valuable for
representing global and local properties of molecules, such as electrostatic potential.
Graphics can also be animated to represent molecular processes and chemical reactions, a
feat that is not easy to reproduce physically.

History

Initially the rendering was on early CRT screens or through plotters drawing on paper.
Molecular structures have always been an attractive choice for developing new computer
graphics tools, since the input data are easy to create and the results are usually highly
appealing. The first example of MG was a display of a protein molecule (Project MAC, 1966)
by Cyrus Levin thai and Robert Langridge. Among the milestones in high-performance MG
was the work of Nelson Max in "realistic" rendering of macromolecules using reflecting
spheres.

By about 1980 many laboratories both in academia and industry had recognized the power
of the computer to analyse and predict the properties of molecules, especially in materials
science and the pharmaceutical industry. The discipline was often called "molecular
graphics" and in 1982 a group of academics and industrialists in the UK set up the
Molecular Graphics Society (MGS). Initially much of the technology concentrated either on
high-performance 3D graphics, including interactive rotation or 3D rendering of atoms as
spheres (sometimes with radiosity). During the 1980s a number of programs for calculating
molecular properties (such as molecular dynamics and quantum mechanics) became
available and the term "molecular graphics" often included these. As a result the MGS has
now changed its name to the Molecular Graphics and Modelling Society (MGMS).

The requirements of macromolecular crystallography also drove MG because the traditional
techniques of physical model-building could not scale. Alwyn Jones' FRODO program (and
later "O") were developed to overlay the molecular electron density determined from X-ray
crystallography and the hypothetical molecular structure.

Molecular graphics

Art, science and technology in molecular graphics

Both computer technology and graphic arts have
contributed to molecular graphics. The development
of structural biology in the 1950s led to a
requirement to display molecules with thousands of
atoms. The existing computer technology was
limited in power, and in any case a naive depiction
of all atoms left viewers overwhelmed. Most systems
therefore used conventions where information was
implicit or stylistic. Two vectors meeting at a point
implied an atom or (in macromolecules) a complete
residue (10-20 atoms).

The macromolecular approach was popularized by
Dickerson and Geis' presentation of proteins and the
graphic work of Jane Richardson through
high-quality hand-drawn diagrams such as the
"ribbon" representation. In this they strove to
capture the intrinsic 'meaning' of the molecule. This
search for the "messages in the molecule" has
always accompanied the increasing power of
computer graphics processing. Typically the
depiction would concentrate on specific areas of the
molecule (such as the active site) and this might
have different colours or more detail in the number
of explicit atoms or the type of depiction (e.g.,
spheres for atoms).

Fig. 2. Image of hemagglutinin with alpha

helices depicted as cylinders and the rest

of the chain as silver coils. The individual

protein atoms (several thousand) have

been hidden. All of the non-hydrogen atoms

in the two ligands (presumably sialic acid)

have been shown near the top of the

diagram. Key: Carbon = grey, oxygen =

red, nitrogen = blue.

In some cases the limitations of technology have led
to serendipitous methods for rendering. Most early graphics devices used vector graphics,
which meant that rendering spheres and surfaces was impossible. Michael Connolly's
program "MS" calculated points on the surface-accessible surface of a molecule, and the
points were rendered as dots with good visibility using the new vector graphics technology,
such as the Evans and Sutherland PS300 series. Thin sections ("slabs") through the
structural display showed very clearly the complementarity of the surfaces for molecules
binding to active sites, and the "Connolly surface" became a universal metaphor.

The relationship between the art and science of molecular graphics is shown in the

T31

exhibitions sponsored by the Molecular Graphics Society. Some exhibits are created with
molecular graphics programs alone, while others are collages, or involve physical materials.
An example from Mike Hann (1994), inspired by Magritte's painting Ceci n'est pas une
pipe, uses an image of a salmeterol molecule.

"Ceci n'est pas une molecule," writes Mike Hann, "serves to remind us that all of the
graphics images presented here are not molecules, not even pictures of molecules, but
pictures of icons which we believe represent some aspects of the molecule's properties."

Molecular graphics

Space-filling models

Fig. 4 is a "space-filling" representation of formic acid,

where atoms are drawn to suggest the amount of space

they occupy. This is necessarily an icon: in the quantum

mechanical representation of molecules, there are only

(positively charged) nuclei and a "cloud" of negative

electrons. The electron cloud defines an approximate

size for the molecule, though there can be no single

precise definition of size. For many years the size of

atoms has been approximated by mechanical models

(CPK), where the atoms have been represented by

plastic spheres whose radius (van der Waals radius)

describes a sphere within which "most" of the electron

density can be found. These spheres could be clicked

together to show the steric aspects of the molecule

rather than the positions of the nuclei. Fig. 4 shows the

intricacy required to make sure that all spheres intersect correctly, and also demonstrates

a reflective model.

Fig. 4. Space-filling model of formic

acid. Key: Hydrogen = white, carbon =

black, oxygen = red.

c -^

£\f

pB V^P

Fig. 5. A molecule (zirconocene) where

part (left) is rendered as ball-and-stick

and part Q

-ight) as an isosurface.

Since the atomic radii (e.g. in Fig. 4) are only slightly
less than the distance between bonded atoms, the
iconic spheres intersect, and in the CPK models, this
was achieved by planar truncations along the bonding
directions, the section being circular. When raster
graphics became affordable, one of the common
approaches was to replicate CPK models in silico. It is
relatively straightforward to calculate the circles of
intersection, but more complex to represent a model
with hidden surface removal. A useful side product is
that a conventional value for the molecular volume can
be calculated.

The use of spheres is often for convenience, being
limited both by graphics libraries and the additional effort required to compute complete
electronic density or other space-filling quantities. It is now relatively common to see
images of isosurfaces that have been coloured to show quantities such as electrostatic
potential. The commonest isosurfaces are the Connolly surface, or the volume within which
a given proportion of the electron density lies. The isosurface in Fig. 5 appears to show the
electrostatic potential, with blue colours being negative and red/yellow (near the metal)
positive. (There is no absolute convention of colouring, and red/positive, blue/negative are
often confusingly reversed!) Opaque isosurfaces do not allow the atoms to be seen and
identified and it is not easy to deduce them. Because of this, isosurfaces are often drawn
with a degree of transparency.

Molecular graphics 26

Technology

Molecular graphics has always pushed the limits of display technology, and has seen a
number of cycles of integration and separation of compute-host and display. Early systems
like Project MAC were bespoke and unique, but in the 1970s the MMS-X and similar
systems used (relatively) low-cost terminals, such as the Tektronix 4014 series, often over
dial-up lines to multi-user hosts. The devices could only display static pictures but, were
able to evangelize MG. In the late 1970s, it was possible for departments (such as
crystallography) to afford their own hosts (e.g., PDP-11) and to attach a display (such as
Evans & Sutherland's MPS) directly to the bus. The display list was kept on the host, and
interactivity was good since updates were rapidly reflected in the display— at the cost of
reducing most machines to a single-user system.

In the early 1980s, Evans & Sutherland (E&S) decoupled their PS300 display, which
contained its own display information transformable through a dataflow architecture.
Complex graphical objects could be downloaded over a serial line (e.g. 9600 baud) and then
manipulated without impact on the host. The architecture was excellent for high
performance display but very inconvenient for domain-specific calculations, such as
electron-density fitting and energy calculations. Many crystallographers and modellers
spent arduous months trying to fit such activities into this architecture.

The benefits for MG were considerable, but by the later 1980s, UNIX workstations such as
Sun-3 with raster graphics (initially at a resolution of 256 by 256) had started to appear.
Computer-assisted drug design in particular required raster graphics for the display of
computed properties such as atomic charge and electrostatic potential. Although E&S had a
high-end range of raster graphics (primarily aimed at the aerospace industry) they failed to
respond to the low-end market challenge where single users, rather than engineering
departments, bought workstations. As a result the market for MG displays passed to Silicon
Graphics, coupled with the development of minisupercomputers (e.g., CONVEX and Alliant)
which were affordable for well-supported MG laboratories. Silicon Graphics provided a
graphics language, IrisGL, which was easier to use and more productive than the PS300
architecture. Commercial companies (e.g., Biosym, Polygen/MSI) ported their code to
Silicon Graphics, and by the early 1990s, this was the "industry standard".

Stereoscopic displays were developed based on liquid crystal polarized spectacles, and
while this had been very expensive on the PS300, it now became a commodity item. A
common alternative was to add a polarizable screen to the front of the display and to
provide viewers with extremely cheap spectacles with orthogonal polarization for separate
eyes. With projectors such as Barco, it was possible to project stereoscopic display onto
special silvered screens and supply an audience of hundreds with spectacles. In this way
molecular graphics became universally known within large sectors of chemical and
biochemical science, especially in the pharmaceutical industry. Because the backgrounds of
many displays were black by default, it was common for modelling sessions and lectures to
be held with almost all lighting turned off.

In the last decade almost all of this technology has become commoditized. IrisGL evolved to
OpenGL so that molecular graphics can be run on any machine. In 1992, Roger Sayle
released his RasMol program into the public domain. RasMol contained a very
high-performance molecular renderer that ran on Unix/X Window, and Sayle later ported
this to the Windows and Macintosh platforms. The Richardsons developed kinemages and
the Mage software, which was also multi-platform. By specifying the chemical MIME type,

Molecular graphics

molecular models could be served over the Internet, so that for the first time MG could be
distributed at zero cost regardless of platform. In 1995, Birkbeck College's crystallography
department used this to run "Principles of Protein Structure", the first multimedia course
on the Internet, which reached 100 to 200 scientists.

Fig. 6. A molecule of Porin (protein) shown without ambient occlusion (left) and with (right). Advanced rendering
effects can improve the comprehension of the 3D shape of a molecule.

MG continues to see innovation that balances technology and art, and currently zero-cost or
open source programs such as PyMOL and Jmol have very wide use and acceptance.

Recently the wide spread diffusion of advanced graphics hardware, has improved the
rendering capabilities of the visualization tools. The capabilities of current shading
languages allow the inclusion of advanced graphic effects (like ambient occlusion, cast
shadows and non-photorealistic rendering techniques) in the interactive visualization of
molecules. These graphic effects, beside being eye candy, can improve the comprehension
of the three dimensional shapes of the molecules. An example of the effects that can be
achieved exploiting recent graphics hardware can be seen in the simple open source
visualization system QuteMol.

Algorithms

Reference frames

Drawing molecules requires a transformation between molecular coordinates (usually, but
not always, in Angstrom units) and the screen. Because many molecules are chiral it is
essential that the handedness of the system (almost always right-handed) is preserved. In
molecular graphics the origin (0, 0) is usually at the lower left, while in many computer
systems the origin is at top left. If the z-coordinate is out of the screen (towards the viewer)
the molecule will be referred to right-handed axes, while the screen display will be
left-handed.

Molecular transformations normally require:

• scaling of the display (but not the molecule).

• translations of the molecule and objects on the screen.

• rotations about points and lines.

Conformational changes (e.g. rotations about bonds) require rotation of one part of the
molecule relative to another. The programmer must decide whether a transformation on the

Molecular graphics

screen reflects a change of view or a change in the molecule or its reference frame.

Simple

Fig. 7. Stick model of caffeine drawn in
Jmol.

In early displays only vectors could be drawn e.g. (Fig.
7) which are easy to draw because no rendering or
hidden surface removal is required.

On vector machines the lines would be smooth but on
raster devices Bresenham's algorithm is used (note the
"jaggies" on some of the bonds, which can be largely
removed with antialiasing software.)

Atoms can be drawn as circles, but these should be
sorted so that those with the largest z-coordinates
(nearest the screen) are drawn last. Although
imperfect, this often gives a reasonably attractive
display. Other simple tricks which do not include
hidden surface algorithms are:

• colouring each end of a bond with the same colour as the atom to which it is attached
(Fig. 7).

• drawing less than the whole length of the bond (e.g. 10%-90%) to simulate the bond
sticking out of a circle.

• adding a small offset white circle within the circle for an atom to simulate reflection.

Typical pseudocode for creating Fig. 7 (to fit the molecule exactly to the screen):

Molecular graphics

Note that this assumes the origin is in the bottom left corner of the screen, with Y up the
screen. Many graphics systems have the origin at the top left, with Y down the screen. In
this case the lines (1) and (2) should have the y coordinate generation as:

yO = yScreenMax - (yOf f set+atom0.getY( )*scale) // (1)
yl = yScreenMax - (yOf f set+atoml. getY( )*scale) // (2)

Changes of this sort change the handedness of the axes so it is easy to reverse the chirality
of the displayed molecule unless care is taken.

Advanced

For greater realism and better comprehension of the 3D structure of a molecule many
computer graphics algorithms can be used. For many years molecular graphics has
stressed the capabilities of graphics hardware and has required hardware-specific
approaches. With the increasing power of machines on the desktop, portability is more
important and programs such as Jmol have advanced algorithms that do not rely on
hardware. On the other hand recent graphics hardware is able to interactively render very
complex molecule shapes with a quality that would not be possible with standard software
techniques.

Chronology

This table provides an incomplete chronology of molecular graphics advances.

Developer(s)

Approximate
date

Technology

Comments

Crystallographers

< 1960

Hand-drawn

Crystal structures, with hidden atom
and bond removal. Often clinographic
projections.

Cyrus Levinthal, Bob
Langridge

1960s

CRT

First protein display on screen (Project
MAC).

Johnson, Motherwell

ca 1970

Pen plotter

ORTEP, PLUTO. Very widely deployed
for publishing crystal structures.

Langridge, White,
Marshall

Late 1970s

Departmental systems
(PDP-11, Tektronix
displays or DEC-VT11, e.g.
MMS-X)

Mixture of commodity computing with
early displays.

T. Alwyn Jones

1978

FRODO

Crystallographic structure solution.

Davies, Hubbard

Mid-1980s

CHEM-X, HYDRA

Laboratory systems with multicolor,
raster and vector devices (Sigmex,
PS300).

Biosym, Tripos, Polygen

Mid-1980s

PS300 and lower cost
dumb terminals (VT200,
SIGMEX)

Commercial integrated modelling and
display packages.

Silicon Graphics, Sun

Late 1980s

IRIS GL (UNIX)
workstations

Commodity-priced single-user
workstations with stereoscopic
display.

EMBL - WHAT IF [4]

1989, 2000

Machine independent

Nearly free, multifunctional, still fully
supported, many free servers
based on it

Molecular graphics

Sayle, Richardson

1992, 1993

RasMol, Kinemage

Platform-independent MG.

MDL (van Vliet, Maffett,
Adler, Holt)

1995-1998

Chime

proprietary C++ ; free browser plugin
for Mac (OS9) and PCs

ChemAxon

1998-

MarvinSketch [6] &

[7]
MarvinView

MarvinSpace [8] (2005)

proprietary Java applet or stand-alone
application.

Community efforts

2000-

Jmol, PyMol, Protein
Workshop (www.pdb.org)

Open-source Java applet or
stand-alone application.

San Diego Supercomputer
Center

2006-

Sirius

Free for academic/non-profit
institutions

NOCH

2002-

NOC [9]

Powerful and open source code
molecular structure explorer

Weizmann Institute of
Science - Community
efforts

2008-

Proteopedia

Collaborative, 3D wiki encyclopedia of
proteins & other molecules

References

[1] Dickerson, R.E.; Geis, I. (1969). The structure and action of proteins. Menlo Park, CA: W.A. Benjamin.

[2] International Union of Pure and Applied Chemistry (1997). " molecular graphics (http://goldbook.iupac.org/

MT06970.html)". Compendium of Chemical Terminology Internet edition.

[3] http://www.scripps.edu/mb/goodsell/mgs_art/

[4] http://swift.cmbi.ru.nl/whatif/

[5] http://swift.cmbi.ru.nl/

[6] http ://www. chemaxon. com/product/msketch.html

[7] http ://www. chemaxon. com/product/mview. html

[8] http://www.chemaxon.com/product/mspace.html

[9] http://noch.sourceforge.net

See also

• Molecular Design software

• Molecular model

• Molecular modelling

• Molecular geometry

• Software for molecular mechanics modeling

External links

• The PyMOL Molecular Graphics System (http://pymol.sf.net) -- open source

• PyMOLWiki (http://pymolwiki.org) -- community supported wiki for PyMOL

• History of Visualization of Biological Macromolecules (http://www.umass.edu/
microbio/rasmol/history.htm) by Eric Martz and Eric Francoeur.

• Brief History of Molecular Mechanics/Graphics (http://stanley.chem.lsu.edu/webpub/
7770-Lecture-l-intro.pdf) in LSU CHEM7770 lecture notes.

• Historical slides (http://luminary.stanford.edu/langridge/slides.htm) from Robert
(Bob) Langridge. These show the influence of Crick and Watson on molecular graphics
(including Levinthal's) and the development of early display technology, finishing with
displays which were common in the mid-1980s on machines such as Evans and

Molecular graphics 31

Sutherland's PS300 series.

Interview with Langridge. (http://luminary.stanford.edu/langridge/langridge.html)

The display looking down the axis of B-DNA has been likened to a rose window.

Nelson Max's home page (http://accad.osu.edu/~waynec/history/tree/max.html)

with links to 1982 classics.

Jmol home page (http://jmol.sourceforge.net/) contains an applet with an automatic

display of many features of molecular graphics including metaphors, scripting,

annotation and animation.

Richardson Lab (http://kinemage.biochem.duke.edu/) includes Kinemage and

molecular graphics images.

History of RasMol. (http://www.openrasmol.org/history.html)

Molecule of the Month (http://www.rcsb. org/pdb/static.do?p=education_discussion/

molecule j>f_the_month/index. html) at RCSB/PDB.

xeo (http://sourceforge.net/projects/xeo) xeo is a free (GPL) open project management

for nanostructures using Java

Exhibitions of Molecular Graphics Art (http://www.scripps.edu/mb/goodsell/mgs_art/

), 1994, 1998.

NOCH home page (http://noch.sourceforge.net) A powerful, efficient and open source

molecular graphics tool.

eMovie (http://www.weizmann.ac.il/ISPC/eMovie.html): a tool for creation of

molecular animations with PyMOL.

Proteopedia (http://www.proteopedia.org): The collaborative, 3D encyclopedia of

proteins and other molecules.

Ascalaph Graphics (http://www.agilemolecule.com/Ascalaph/Ascalaph_Graphics.

html): a molecular viewer with some geometry editing capabilities.

Molecular Graphics and Modelling Society, (http://www.mgms.org/)

Journal of Molecular Graphics and Modelling (http://www.sciencedirect.com/

science?_ob=JournalURL&_cdi=5260&_auth=y&_acct=C000053194&_version=l&

_urlVersion=0&_userid=1495569&md5 = le86bcce088e98890cea52f6eda84b64)

(formally Journal of Molecular Graphics). This journal is not open access.

List of software for molecular mechanics modeling

List of software for molecular
mechanics modeling

This is a list of computer programs that are predominantly used for molecular mechanics
calculations.

Min - Optimization, MD - Molecular Dynamics, MC - Monte Carlo, QM - Quantum

mechanics. Imp - Implicit water. HA - Hardware accelerated.

Y - Yes.

I - Has interface.

Name

View
3D

Model
Builder

Min

Imp

Comments

License

Website

Ab alone

Biomolecular
simulations, protein
folding.

Not
free

Agile

Molecule
[1]

ACEMD [ '

Molecular
dynamics with
CHARMM, Amber
forcefields.
Running on NVIDIA
GPUs. Heavily
optimized with
CUDA.

Not
free

Acellera Ltd
[3]

AMBER [ '

Not
free

ambermd.orc
[5]

Ascalaph
Designer

Molecular building

(DNA, proteins,

hydrocarbons,

nanotubes).

Molecular

dynamics. GPU

acceleration.

Free

Comme

Ascalaph

Project [6]
rcial

Balloon

2D/3D conversion
and conformational
analysis.

Free

use,

closed

source

Abo

T71
Akademi

BOSS

OPLS

Comme

University
[8]

CHARM IN

Commercial version
with multiple
graphical front
ends is sold by
Accelrys (as
CHARMm)

Not
free

charmm.org
[9]

List of software for molecular mechanics modeling

ChemSketth Y

Fast 2-D graphical
molecule builder
and 3-D viewer.
Contains simplified
CHARMM for fast
stable inaccurate
optimization of
single molecules up
to 1000 atoms

Advanced
Chemistry
Development

Inc.

COSMOS Y

Desmond

Hybrid QM/MM
COSMOS-NMR
force field with fast
semi-empirical
calculation of
electrostatic and/or
NMR properties.
3-D graphical
molecule builder
and viewer.

High Performance
MD.

Free

( without
GUI)
and
commercial

COSMOS

oftware
[11]

Free
and

comme rfclafl

D. E. Shaw
Research

GoVASP

I I

GROMACS

GROMOS

GoVASP is a
sophisticated
graphical user
interface for the
Vienna Ab-initio
Simulation Package
(VASP). GoVASP
comprises tools to
prepare, perform
and monitor VASP
calculations and to
evaluate and
visualize the
computed data.

High performance
MD

Geared towards
biomolecules

Closed
source.

Windiks

/t C°o t nsulting
free/Tria~]13]

available

Free

Not
free

gromacs.org
fl4]

LAMMPS

MacroMoYel Y

Has potentials for Free
soft and solid-state
materials and
coarse-grain
systems

OPLS-AA, GBSA Not

solvent model, free

conformational
sampling,
minimization, MD

Sandia

[15]

Schrodinger,
LLC [16]

List of software for molecular mechanics modeling

Materials
Studio

Materials Studio is
a software
environment that
brings the
materials
simulation
technology to
desktop computing,
solving key
problems
throughout the
R&D process.

Closed
source,
available

Accelrys

MedeA

MCCCS
Towhee

MedeA combines
leading
experimental
databases and
major

computational
programs like the
Vienna Ab-initio
Simulation Package
(VASP) with
sophisticated
materials property
prediction,
analysis, and
visualization.

Originally designed
for the prediction
of fluid phase
eguilibria

link

Closed

source/[Not

free

[18]

Free

Towhee
Project

[19]

MDynaMix

[20]

MOE

MOIL

Y Y Y Y

Parallel MD

Molecular
Operating
Environment

Also includes
action-based
algorithms
(Stochastic
Difference
Eguation in Time
and Stochastic
Difference
Eguation in Length)
and locally
enhanced sampling.

Free

Stockholm

University
[21]

Commep

Comical

itini
[221

Computing
■J

Free

Group
hnk^l

molecoolsY Y

MOLDY

Simple Javascript
molecular
visualization tool

Parallel, only
pair-potentials, Cell
lists, modified
Beeman's algorithm

link

[24]

Free

Moldy

[25]

List of software for molecular mechanics modeling

NAB [26]

Generation of
Models for
"Unusual" DNA and
RNA

Free

Case group
[27]

Packmol

Builds complex
initial

configurations for
Molecular
Dynamics

link [28]

Prime

Homology
modeling, loop and
side chain
optimization,
minimization,
OPLS-AA, SGB
solvent model,
parallalized

link [29]

Protein
Local
Optimiza
Program

tion

Helix, loop, and
side chain
optimization. Fast
energy
minimization.

Not
free

link [30]

QMOL

Protein viewer

Free

DNASTAR,

, [31]
Inc.

RasMol

Fast viewer

Free

RasMol [32]

Raster 3D

High quality raster
images

Free

University

Washinqton
[33]

STR3DI3

Sophisticated 3-D
molecule builder
and viewer,
advanced
structural
analytical
algorithms, full
featured molecular
modeling and
quantitation of
stereo-electronic
effects, docking
and the handling of
complexes.

The

200
atom
version
is free

Exorqa, Inc.
[34]

Selvita
Protein
Modeling
Platform

Protein structure
prediction,
homology
modeling, ab initio
modeling, loop
modeling, protein
threading

Comme

r §Svita Ltd
[35]

TINKER

Software Tools for
Molecular Design

Free

Washinqton

University
[36]

List of software for molecular mechanics modeling

UCSF
Chimera

Visually appealing
viewer, amino acid
rotamers and other
building, includes
Antechamber and
MMTK, Ambertools
plugins in
development.

University

of California
[37]

VMD +
NAMD

Fast, parallel MD

Free

Beckman

Institute
[38]

WHAT
IF

Visualizer for MD.
Interface to
GROMACS.

Not
free

WHAT IF
[4]

xeo

open project
management for
nanostructures

link [39]

YASARA

Molecular-graphics,
-modeling and
-simulation
program

Not
free

YASARA.org
[40]

Zodiac

Drug design suite

lmk [41]

See also

Molecular dynamics

Molecular Design software

Molecule editor

Molecular modeling on GPU

Quantum chemistry computer programs

List of nucleic acid simulation software

List of protein structure prediction software

Force field implementation

External links

SINCRIS [42]

Linux4Chemistry

Collaborative Computational Project

World Index of Molecular Visualization Resources

[43]

[44]

[46]

Short list of Molecular Modeling resources
OpenScience [ 7]

Biological Magnetic Resonance Data Bank ^ '
Materials modelling and computer simulation codes ^ *

List of software for molecular mechanics modeling

References

[ 1 ] http ://www. agilemolecule. com/Abalone/index. html

[2] M. J. Harvey, G. Giupponi and G. De Fabritiis (2009). "ACEMD: Accelerating Biomolecular Dynamics in the

Microsecond Time Scale". Journal of Chemical THeory and Computation: ASAP.
[ 3 ] http ://www. acellera. com/index. php?arg= acemd
[4] Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM Jr, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW,

Kollman PA (1995). "A second generation force field for the simulation of proteins, nucleic acids, and organic

molecules"./. Am. Chem. Soc. 117: 5179-5197. doi: 10.1021/ja00124a002 (http://dx.doi.org/10.1021/

ja00124a002).
[5] http://ambermd.org

[6] http://www.agilemolecule.com/Ascalaph/Packages.html
[7] http://www.abo.fi/~mivainio/balloon/
[8] http ://zarbi. chem. yale.edu/software. html#boss
[9] http://www.charmm.org/

[10] http ://www. acdlabs.com/products/chem_dsn_lab/chemsketch/
[11] http ://www. cosmos-software. de/ce_intro. html
[12] http://deshawresearch.com/resources.html
[13] http://www.govasp.com
[14] http://www.gromacs.org
[15] http://lammps.sandia.gov/

[16] http://www.schrodinger.com/ProductDescription.php?mID=6&sID=8&cID=0
[17] http ://accelrys .com/products/materials-studio/
[18] http ://www. materialsdesign. com/products. htm
[19] http ://towhee. sourceforge. net/
[20] Lyubartsev AP, Laaksonen A (2000). "MDynaMix - A scalable portable parallel MD simulation package for

arbitrary molecular mixtures". Computer Physics Communications 128: 565-589. doi:

10.1016/S0010-4655(99)00529-9 (http://dx.doi.org/10. 1016/S0010-4655(99)00529-9).
[21] http://www.fos.su.se/~sasha/mdynamix/
[22] http://www.chemcomp.com/

[23] http://cbsu.tc.cornell.edu/software/moil/moil.html
[24] http://blahbleh.com/molecools.php
[25] http://www.ccp5.ac.uk/moldy/moldy.html
[26] Macke T, Case DA (1998). "Modeling unusual nucleic acid structures". Molecular Modeling of Nucleic Acids:

379-393.
[27] http://www.scripps.edu/mb/case/
[28] http://www.ime.unicamp.br/~martinez/packmol

[29] http://www.schrodinger.com/ProductDescription.php?mID=6&sID=2&cID=0
[30] http://jacobson.compbio.ucsf.edu/plop_manual/plop_overview.htm
[31] http ://www. dnastar. com/products/gmol/index. html
[32] http://www.bernstein-plus-sons.com/software/rasmol/
[33] http ://skuld. bmsc. Washington. edu/raster3d/raster3d. html
[34] http://www.exorga.com

[35] http://www.selvita.com/selvita-protein-modeling-platform.html
[36] http://dasher.wustl.edu/tinker/
[37] http://www.cgl.ucsf.edu/chimera/index.html
[38] http://www.ks.uiuc.edu/Research/vmd/
[39] http://sourceforge.net/projects/xeo
[40] http://www.yasara.com/
[41] http://www.zeden.org/

[42] http://wwl.iucr.org/sincris-top/logiciel/abc.html
[43] http://www.redbrick.dcu.ie/~noel/linux4chemistry/
[44] http ://www. ccp 1 4 . ac.uk/mirror/mirror. htm
[45] http://molvis.sdsc.edu/visres/index.html
[46] http://www.agilemolecule.com/Software.html
[47] http://www.openscience.org/links/index.php?section=7
[48] http://www.bmrb.wisc.edu/www/software.html
[49] http ://www. sklogwiki. org/SklogWiki/index. php/

Category:Materials_modelling_and_computer_simulation_codes

List of software for molecular mechanics modeling 38

Molecular Modeling Applications
to Complex Biomolecules

Protein structure prediction

Protein structure prediction is the prediction of the three-dimensional structure of a
protein from its amino acid sequence— that is, the prediction of a protein's tertiary
structure from its primary structure. It is one of the most important goals pursued by
bioinformatics and theoretical chemistry. Protein structure prediction is of high importance
in medicine (for example, in drug design) and biotechnology (for example, in the design of
novel enzymes). Every two years, the performance of current methods is assessed in the
CASP experiment.

The practical role of protein structure prediction is now more important than ever. Massive
amounts of protein sequence data are produced by modern large-scale DNA sequencing
efforts such as the Human Genome Project. Despite community-wide efforts in structural
genomics, the output of experimentally determined protein structures— typically by
time-consuming and relatively expensive X-ray crystallography or NMR spectroscopy— is
lagging far behind the output of protein sequences.

A number of factors exist that make protein structure prediction a very difficult task. The
two main problems are that the number of possible protein structures is extremely large,
and that the physical basis of protein structural stability is not fully understood. As a result,
any protein structure prediction method needs a way to explore the space of possible
structures efficiently (a search strategy), and a way to identify the most plausible structure
(an energy function).

In comparative structure prediction (also called homology modeling), the search space is
pruned by the assumption that the protein in question adopts a structure that is reasonably
close to the structure of at least one known protein. In de novo or ab initio structure
prediction, no such assumption is made, which results in a much harder search problem. In
both cases, an energy function is needed to recognize the native structure, and to guide the
search for the native structure. Unfortunately, the construction of such an energy function
is to a great extent an open problem.

Direct simulation of protein folding in atomic detail, via methods such as molecular
dynamics with a suitable energy function, is typically not tractable due to the high
computational cost, despite the efforts of distributed computing projects such as
Folding@home. Therefore, most de novo structure prediction methods rely on simplified
representations of the atomic structure of proteins.

The above mentioned issues apply to all proteins, including well-behaving, small,
monomeric proteins. In addition, for specific proteins (such as for example multimeric
proteins and disordered proteins), the following issues also arise:

• Some proteins require stabilisation by additional domains or binding partners to adopt
their native structure. This requirement is typically unknown in advance and difficult to
handle by a prediction method.

Protein structure prediction 39

• The tertiary structure of a native protein may not be readily formed without the aid of
additional agents. For example, proteins known as chaperones are required for some
proteins to properly fold. Other proteins cannot fold properly without modifications such
as glycosylation.

• A particular protein may be able to assume multiple conformations depending on its
chemical environment.

• The biologically active conformation may not be the most thermodynamically favorable.

Due to the increase in computer power, and especially new algorithms, much progress is
being made to overcome these problems. However, routine de novo prediction of protein
structures, even for small proteins, is still not achieved.

Ab initio protein modelling

Ab initio- or de novo- protein modelling methods seek to build three-dimensional protein
models "from scratch", i.e., based on physical principles rather than (directly) on previously
solved structures. There are many possible procedures that either attempt to mimic protein
folding or apply some stochastic method to search possible solutions (i.e., global
optimization of a suitable energy function). These procedures tend to require vast
computational resources, and have thus only been carried out for tiny proteins. To predict
protein structure de novo for larger proteins will require better algorithms and larger
computational resources like those afforded by either powerful supercomputers (such as
Blue Gene or MDGRAPE-3) or distributed computing (such as Folding@home, the Human
Proteome Folding Project and Rosetta@Home). Although these computational barriers are
vast, the potential benefits of structural genomics (by predicted or experimental methods)
make ab initio structure prediction an active research field

As an intermediate step towards predicted protein structures, contact map predictions have
been proposed.

Comparative protein modelling

Comparative protein modelling uses previously solved structures as starting points, or
templates. This is effective because it appears that although the number of actual proteins
is vast, there is a limited set of tertiary structural motifs to which most proteins belong. It
has been suggested that there are only around 2000 distinct protein folds in nature, though
there are many millions of different proteins.

These methods may also be split into two groups :

• Homology modeling is based on the reasonable assumption that two homologous
proteins will share very similar structures. Because a protein's fold is more evolutionarily
conserved than its amino acid sequence, a target sequence can be modeled with
reasonable accuracy on a very distantly related template, provided that the relationship
between target and template can be discerned through sequence alignment. It has been
suggested that the primary bottleneck in comparative modelling arises from difficulties in
alignment rather than from errors in structure prediction given a known-good
alignment. Unsurprisingly, homology modelling is most accurate when the target and

template have similar sequences.

Protein threading scans the ai

database of solved structures. In each case, a scoring function is used to assess the

• Protein threading scans the amino acid sequence of an unknown structure against a

Protein structure prediction 40

compatibility of the sequence to the structure, thus yielding possible three-dimensional
models. This type of method is also known as 3D-1D fold recognition due to its
compatibility analysis between three-dimensional structures and linear protein
sequences. This method has also given rise to methods performing an inverse folding
search by evaluating the compatibility of a given structure with a large database of
sequences, thus predicting which sequences have the potential to produce a given fold.

Side chain geometry prediction

Even structure prediction methods that are reasonably accurate for the peptide backbone
often get the orientation and packing of the amino acid side chains wrong. Methods that
specifically address the problem of predicting side chain geometry include dead-end
elimination and the self-consistent mean field method. Both discretize the continuously
varying dihedral angles that determine a side chain's orientation relative to the backbone
into a set of rotamers with fixed dihedral angles. The methods then attempt to identify the
set of rotamers that minimize the model's overall energy. Rotamers are the side chain
conformations with low energy. Such methods are most useful for analyzing the protein's
hydrophobic core, where side chains are more closely packed; they have more difficulty
addressing the looser constraints and higher flexibility of surface residues.

Protein-protein complexes

In the case of complexes of two or more proteins, where the structures of the proteins are
known or can be predicted with high accuracy, protein-protein docking methods can be
used to predict the structure of the complex. Information of the effect of mutations at
specific sites on the affinity of the complex helps to understand the complex structure and
to guide docking methods.

Software

MODELLER is a popular software tool for producing homology models using methodology
derived from NMR spectroscopy data processing. SwissModel provides an automated
web server for basic homology modeling. I-TASSER is the best server for protein
structure prediction according to the recent CASP experiments (CASP7 [ ] and CASP8

). Common software tools for protein threading are HHpred / HHsearch, bioinfo.pl
Robetta , and Phyre . RAPTOR (software) is a protein threading software that is
based on integer programming. The basic algorithm for threading is described in and is
fairly straightforward to implement. Abalone is a Molecular Dynamics program for
folding simulations with explicit or implicit water models.

Several distributed computing projects concerning protein structure prediction have also
been implemented, such as the Folding@home, Rosetta@home, Human Proteome Folding
Project, Predictor@home and TANPAKU. The Foldit program seeks to investigate the
pattern-recognition and puzzle-solving abilities inherent to the human mind in order to
create more successful computer protein structure prediction software.

Computational approaches provide a fast alternative route to antibody structure prediction.
Recently developed antibody F region high resolution structure prediction algorithms like
RosettaAntibody ( http://antibody.graylab.jhu.edu ) have been shown to generate high

MO]

resolution homology models which have been used for successful docking. J

Protein structure prediction 41

Reviews of software for structure prediction can be found at. The progress and

rn
challenges in protein structure prediction has been reviewed in .

Automatic structure prediction servers

CASP, which stands for Critical Assessment of Techniques for Protein Structure Prediction,
is a community-wide experiment for protein structure prediction taking place every two
years since 1994. CASP provides users and research groups with an opportunity to assess
the quality of available methods and automatic servers for protein structure prediction.
Official results for automatic structure prediction servers in the CASP7 benchmark (2006)
are discussed by Battey at al.: . Official CASP8 results are available here
Preliminary, unofficial results for automatic servers of the recent CASP8 benchmark are
summarized on several lab websites and ranked according to slightly varying criteria:
Zhang lab [17] , Grishin lab [18] , McGuffin lab [19] , Baker lab [20] , Cheng lab [21]

See also

• Protein design

• Protein structure prediction software

• Protein-protein interaction prediction

• Molecular modeling software

• CASP: Annual Protein Structure Prediction Competition

References

[I] Zhang Y (2008). "Progress and challenges in protein structure prediction". Curr Opin Struct Biol 18 (3):
342-348. doi: 10.1016/j.sbi.2008.02.004 (http://dx.doi.Org/10.1016/j.sbi.2008.02.004). Entrez Pubmed
18436442 (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&
list_uids=18436442). PMID 18436442.

[2] Zhang Y and Skolnick J (2005). "The protein structure prediction problem could be solved using the current
PDB library". Proc Natl Acad Sci USA 102 (4): 1029-1034. doi: 10. 1073/pnas. 0407152101 (http://dx.doi.org/
10. 1073/pnas. 0407152101). Entrez Pubmed 15653774 (http://www.ncbi.nlm.nih.gov/entrez/query.
fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=l 5653774). PMID 15653774.

[3] Bowie JU, Luthy R, Eisenberg D (1991). "A method to identify protein sequences that fold into a known
three-dimensional structure". Science 253 (5016): 164-170. doi: 10.1 126/science. 1853201 (http://dx.doi.org/
10. 1126/science. 1853201). Entrez Pubmed 1853201 (http://www.ncbi.nlm.nih.gov/entrez/query.
fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=l 853201). PMID 1853201.

[4] Voigt CA, Gordon DB, Mayo SL (2000). "Trading accuracy for speed: A quantitative comparison of search
algorithms in protein sequence design". J Mol Biol 299 (3): 789-803. doi: 10.1006/jmbi.2000.3758 (http : //dx.
doi.org/10.1006/jmbi.2000.3758). Entrez Pubmed 10835284 (http://www.ncbi.nlm.nih.gov/entrez/
query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids= 1083 5284).

[5] http://swissmodel.expasy.Org//SWISS-MODEL.html

[6] http://zhang.bioinformatics.ku.edu/I-TASSER

[7] http://predictioncenter.org

[8] http://www.predictioncenter.org/casp7/Casp7.html

[9] http://www.predictioncenter.org/casp8/index.cgi

[10] http://meta.bioinfo.pl/submit_wizard.pl

[II] http ://robetta. bakerlab . org/

[12] http ://www. sbg. bio. ic. ac. uk/phyre/index. cgi

[13] Sivasubramanian A, Sircar A, Chaudhury S, Gray J J (2009). "Toward high-resolution homology modeling of

antibody Fv regions and application to antibody-antigen docking". Proteins 74: 497-514. doi:

10.1002/prot.22309 (http://dx.doi.org/10.1002/prot.22309).
[14] Nayeem A, Sitkoff D, Krystek S Jr (2006). "A comparative study of available software for high-accuracy

homology modeling: From sequence alignments to structural models". Protein Sci 15: 808-824. doi:

10. 1110/ps. 051892906 (http://dx.doi.org/10.1110/ps.051892906). Entrez Pubmed 16600967 (http://www.

Protein structure prediction 42

ncbi.nlm.nih. gov/ entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids= 16600967).

PMID 16600967.
[15] Battey JN, Kopp J, Bordoli L, Read RJ, Clarke ND, Schwede T (2007). "Automated server predictions in

CASP7". Proteins 69 (Suppl 8): 68-82.. PMID 17894354.
[ 1 6] http ://predictioncenter. org/casp8/results. cgi
[17] http ://zhang. bioinformatics .ku. edu/casp8/index. html
[18] http ://prodata. swmed. edu/CASP8/evaluation/DomainsAll. First.html
[19] http ://www. reading. ac. uk/bioinf/CASP8/index. html
[20] http://robetta.bakerlab.org/CASP8_eval_domains/
[21] http://sysbio.rnet.missouri.edu/casp8_eva/

External links

• CASP experiments home page (http://predictioncenter.org/)

• Structure Prediction Flowchart (a clickable map) (http://www.russell.embl-heidelberg.
de/gtsp/flowchart2 .html)

Protein design

Protein design is the design of new protein molecules from scratch, or the deliberate
design of a new molecule by making calculated variations on a known structure. The
number of possible amino acid sequences is enormous, but only a subset of these sequences
will fold reliably and quickly to a single native state. Protein design involves identifying
such sequences, in particular those with a physiologically active native state. Protein design
is a rational design technique used in protein engineering.

Protein design requires an understanding of the molecular interactions that stabilize
proteins in specific folded configurations fold; experience has shown, however, that protein
design does not require an understanding of the dynamical process by which proteins fold.
In a sense it is the reverse of structure prediction: a tertiary structure is specified, and an
amino acid sequence is identified which will fold to it.

Protein design is also referred to as inverse folding. From a physical point of view, the
native state conformation of a protein is the free energy minimum for the protein chain.
Hence, designing a new protein involves the identification of the sequences which have the
chosen structure as free energy minimum. This can be done by use of computer models,
which, while simplifying the problem, are able to generate sequences to fold on the desired
structure.

The design of minimalist computer models of proteins (lattice proteins), and the secondary
structural modification of real proteins, began in the mid-1990s. The de novo design of real
proteins became possible shortly afterwards, and the 21st century has seen the creation of
small proteins with real biological function including catalysis and antiviral behaviour.
There is great hope that the design of these and larger proteins will have application in
medicine and bioengineering.

Computational protein design algorithms seek to identify amino acid sequences that have
low energies for target structures. While the sequence-conformation space that needs to be
searched is large, the most challenging requirement for computational protein design is a
fast, yet accurate, energy function that can distinguish optimal sequences from similar
suboptimal ones. Using computational methods, a protein with a novel fold has been
designed[l], as well as sensors for un-natural molecules[2].

Protein design 43

On the other hand, it is widely believed that not all possible protein structures are
designable, which means that there are compact configurations of the chain which no
sequences can fold to. In particular, conformations which are poor in secondary structures
are unlikely to be designable. The designability of given structures is still an issue that is
poorly understood.

Models of protein structure and function used in protein
design

Computational protein design algorithms use models of

protein energetics to evaluate how mutations would

affect a protein's structure and function. These energy

functions typically include a combination of molecular

mechanics, knowledge-based, and other empirical

terms. However, the trend has been towards using Comparison of various potential

r-j-i energy functions
more physically based potential energy functions. 1 J |

Software

EGAD: A Genetic Algorithm for protein Design[4]. A free, open-source software
package for protein design and prediction of mutation effects on protein folding stabilities
and binding affinities. EGAD can also consider multiple structures simultaneously for
designing specific binding proteins or locking proteins into specific conformational states.
In addition to natural protein residues, EGAD can also consider free-moving ligands with or
without rotatable bonds. EGAD can be used with single or multiple processors.

r cr "I

SHARPEN . A permissive open-source library for protein design and structure
prediction. SHARPEN offers a variety of combinatorial optimization methods (e.g. Monte
Carlo, Simulated Annealing, FASTER ) and can score proteins using the successful
Rosetta all-atom force field or molecular mechanics force fields (OPLSaa). In addition to the
protein modeling library, SHARPEN includes tools for scalable distributed computing.

WHAT IF software for protein modelling, design, validation, and visualisation.

Abalone software for protein modelling and visualisation.

References

• B.I.DAHIYAT and S.L. MAYO, De Novo Protein Design: Fully Automated Sequence
Selection, Science 3 October 1997:Vol. 278. no. 5335, pp. 82 - 87

• C. Sander, G. Vriend, et al., Protein Design on computers. Five new proteins: Shpilka,
Grendel, Fingerclasp, Leather and Aida. PROTEINS 12, 105-110 (1992).

• Jin et al., Structure, 11, 581 (2003).

• Nagai et al., Proc. Natl. Acad. Sci. USA, 98, 3197 (2001).

• Saghatelian et al., Nature, 409, 797 (2001).

• Kuhlman et al. "Science", 302:1364 (2003)[1]

• Looger et al. "Nature", 423:185 (2003)[2]

• Pokala and Handel "J Mol Biol", 347:203 (2005)[7]

[1] http://www.sciencemag.org/cgi/content/full/302/5649/1364

[2] http://www.nature.com/nature/journal/v423/n6936/abs/nature01556.html

Protein design 44

[3] Boas, F. E. & Harbury, P. B. (2007). "Potential energy functions for protein design." Curr. Opin. Struct. Biol.
17, 199-204. (http://www.ncbi.nlm.nih.gov/pubmed/17387014)

[4] http

[5] http

[6] http

[7] http

//egad. ucsd.edu/EGAD_manual/index. html
//www. sharp-n. com

//www.ncbi. nlm.nih.gov/pubmed/1201 2335
//dx. doi. org/10. 1016/j.jmb. 2004. 12.019

See also

• PEGylation

• Protein structure prediction software

• Software for molecular modeling

Homology modeling

Homology modeling, also known as comparative modeling of protein refers to
constructing an atomic-resolution model of the "target" protein from its amino acid
sequence and an experimental three-dimensional structure of a related homologous protein
(the "template"). Homology modeling relies on the identification of one or more known
protein structures likely to resemble the structure of the query sequence, and on the
production of an alignment that maps residues in the query sequence to residues in the
template sequence. The sequence alignment and template structure are then used to
produce a structural model of the target. Because protein structures are more conserved
than DNA sequences, detectable levels of sequence similarity usually imply significant
structural similarity.

The quality of the homology model is dependent on the quality of the sequence alignment
and template structure. The approach can be complicated by the presence of alignment
gaps (commonly called indels) that indicate a structural region present in the target but not
in the template, and by structure gaps in the template that arise from poor resolution in the
experimental procedure (usually X-ray crystallography) used to solve the structure. Model
quality declines with decreasing sequence identity; a typical model has —1-2 A root mean
square deviation between the matched C a atoms at 70% sequence identity but only 2-4 A
agreement at 25% sequence identity. However, the errors are significantly higher in the
loop regions, where the amino acid sequences of the target and template proteins may be
completely different.

Regions of the model that were constructed without a template, usually by loop modeling,
are generally much less accurate than the rest of the model. Errors in side chain packing
and position also increase with decreasing identity, and variations in these packing
configurations have been suggested as a major reason for poor model quality at low

T21

identity. Taken together, these various atomic-position errors are significant and impede
the use of homology models for purposes that require atomic-resolution data, such as drug
design and protein-protein interaction predictions; even the quaternary structure of a
protein may be difficult to predict from homology models of its subunit(s). Nevertheless,
homology models can be useful in reaching qualitative conclusions about the biochemistry
of the query sequence, especially in formulating hypotheses about why certain residues are
conserved, which may in turn lead to experiments to test those hypotheses. For example,
the spatial arrangement of conserved residues may suggest whether a particular residue is
conserved to stabilize the folding, to participate in binding some small molecule, or to

Homology modeling 45

foster association with another protein or nucleic acid.

Homology modeling can produce high-quality structural models when the target and
template are closely related, which has inspired the formation of a structural genomics
consortium dedicated to the production of representative experimental structures for all
classes of protein folds. The chief inaccuracies in homology modeling, which worsen with
lower sequence identity, derive from errors in the initial sequence alignment and from
improper template selection. Like other methods of structure prediction, current practice
in homology modeling is assessed in a biannual large-scale experiment known as the
Critical Assessment of Techniques for Protein Structure Prediction, or CASP.

Motivation

The method of homology modeling is based on the observation that protein tertiary
structure is better conserved than amino acid sequence. Thus, even proteins that have
diverged appreciably in sequence but still share detectable similarity will also share
common structural properties, particularly the overall fold. Because it is difficult and
time-consuming to obtain experimental structures from methods such as X-ray
crystallography and protein NMR for every protein of interest, homology modeling can
provide useful structural models for generating hypotheses about a protein's function and
directing further experimental work.

There are exceptions to the general rule that proteins sharing significant sequence identity
will share a fold. For example, a judiciously chosen set of mutations of less than 50% of a
protein can cause the protein to adopt a completely different fold. However, such a

massive structural rearrangement is unlikely to occur in evolution, especially since the
protein is usually under the constraint that it must fold properly and carry out its function
in the cell. Consequently, the roughly folded structure of a protein (its "topology") is
conserved longer than its amino-acid sequence and much longer than the corresponding
DNA sequence; in other words, two proteins may share a similar fold even if their
evolutionary relationship is so distant that it cannot be discerned reliably. For comparison,
the function of a protein is conserved much less than the protein sequence, since relatively
few changes in amino-acid sequence are required to take on a related function.

Steps in model production

The homology modeling procedure can be broken down into four sequential steps: template
selection, target-template alignment, model construction, and model assessment. The
first two steps are often essentially performed together, as the most common methods of
identifying templates rely on the production of sequence alignments; however, these
alignments may not be of sufficient quality because database search techniques prioritize
speed over alignment quality. These processes can be performed iteratively to improve the
quality of the final model, although quality assessments that are not dependent on the true
target structure are still under development.

Optimizing the speed and accuracy of these steps for use in large-scale automated structure
prediction is a key component of structural genomics initiatives, partly because the
resulting volume of data will be too large to process manually and partly because the goal

of structural genomics requires providing models of reasonable quality to researchers who

rn
are not themselves structure prediction experts.

Homology modeling 46

Template selection and sequence alignment

The critical first step in homology modeling is the identification of the best template
structure, if indeed any are available. The simplest method of template identification relies
on serial pairwise sequence alignments aided by database search techniques such as
FASTA and BLAST. More sensitive methods based on multiple sequence alignment - of
which PSI-BLAST is the most common example - iteratively update their position-specific
scoring matrix to successively identify more distantly related homologs. This family of
methods has been shown to produce a larger number of potential templates and to identify
better templates for sequences that have only distant relationships to any solved structure.
Protein threading, also known as fold recognition or 3D-1D alignment, can also be used as a
search technique for identifying templates to be used in traditional homology modeling
methods. When performing a BLAST search, a reliable first approach is to identify hits
with a sufficiently low E-value, which are considered sufficiently close in evolution to make
a reliable homology model. Other factors may tip the balance in marginal cases; for
example, the template may have a function similar to that of the query sequence, or it may
belong to a homologous operon. However, a template with a poor £ -value should generally
not be chosen, even if it is the only one available, since it may well have a wrong structure,
leading to the production of a misguided model. A better approach is to submit the primary
sequence to fold-recognition servers or, better still, consensus meta-servers which improve
upon individual fold-recognition servers by identifying similarities (consensus) among
independent predictions.

Often several candidate template structures are identified by these approaches. Although
some methods can generate hybrid models from multiple templates, most methods rely on a
single template. Therefore, choosing the best template from among the candidates is a key
step, and can affect the final accuracy of the structure significantly. This choice is guided
by several factors, such as the similarity of the query and template sequences, of their
functions, and of the predicted query and observed template secondary structures. Perhaps
most importantly, the coverage of the aligned regions: the fraction of the query sequence
structure that can be predicted from the template, and the plausibility of the resulting
model. Thus, sometimes several homology models are produced for a single query
sequence, with the most likely candidate chosen only in the final step.

It is possible to use the sequence alignment generated by the database search technique as
the basis for the subsequent model production; however, more sophisticated approaches
have also been explored. One proposal generates an ensemble of stochastically defined
pairwise alignments between the target sequence and a single identified template as a
means of exploring "alignment space" in regions of sequence with low local similarity.
"Profile -profile" alignments that first generate a sequence profile of the target and
systematically compare it to the sequence profiles of solved structures; the coarse-graining
inherent in the profile construction is thought to reduce noise introduced by sequence drift
in nonessential regions of the sequence.

Homology modeling 47

Model generation

Given a template and an alignment, the information contained therein must be used to
generate a three-dimensional structural model of the target, represented as a set of
Cartesian coordinates for each atom in the protein. Three major classes of model
generation methods have been proposed.

Fragment assembly

The original method of homology modeling relied on the assembly of a complete model from
conserved structural fragments identified in closely related solved structures. For example,
a modeling study of serine proteases in mammals identified a sharp distinction between
"core" structural regions conserved in all experimental structures in the class, and variable
regions typically located in the loops where the majority of the sequence differences were
localized. Thus unsolved proteins could be modeled by first constructing the conserved core
and then substituting variable regions from other proteins in the set of solved
structures. Current implementations of this method differ mainly in the way they deal
with regions that are not conserved or that lack a template.

Segment matching

The segment-matching method divides the target into a series of short segments, each of
which is matched to its own template fitted from the Protein Data Bank. Thus, sequence
alignment is done over segments rather than over the entire protein. Selection of the
template for each segment is based on sequence similarity, comparisons of alpha carbon
coordinates, and predicted steric conflicts arising from the van der Waals radii of the
divergent atoms between target and template. [12]

Satisfaction of spatial restraints

The most common current homology modeling method takes its inspiration from
calculations required to construct a three-dimensional structure from data generated by
NMR spectroscopy. One or more target-template alignments are used to construct a set of
geometrical criteria that are then converted to probability density functions for each
restraint. Restraints applied to the main protein internal coordinates - protein backbone
distances and dihedral angles - serve as the basis for a global optimization procedure that
originally used conjugate gradient energy minimization to iteratively refine the positions of
all heavy atoms in the protein/ '

This method had been dramatically expanded to apply specifically to loop modeling, which
can be extremely difficult due to the high flexibility of loops in proteins in aqueous
solution. A more recent expansion applies the spatial-restraint model to electron density
maps derived from cryoelectron microscopy studies, which provide low-resolution

information that is not usually itself sufficient to generate atomic-resolution structural

n 51
models. To address the problem of inaccuracies in initial target-template sequence

alignment, an iterative procedure has also been introduced to refine the alignment on the

basis of the initial structural fit. The most commonly used software in spatial

restraint-based modeling is MODELLER and a database called ModBase has been

ri7i
established for reliable models generated with it.

Homology modeling 48

Loop modeling

Regions of the target sequence that are not aligned to a template are modeled by loop
modeling; they are the most susceptible to major modeling errors and occur with higher
frequency when the target and template have low sequence identity. The coordinates of
unmatched sections determined by loop modeling programs are generally much less
accurate than those obtained from simply copying the coordinates of a known structure,
particularly if the loop is longer than 10 residues. The first two sidechain dihedral angles
(X 1 and x 2 ) can usually be estimated within 30° for an accurate backbone structure;
however, the later dihedral angles found in longer side chains such as lysine and arginine
are notoriously difficult to predict. Moreover, small errors in % (and, to a lesser extent, in
X 2 ) can cause relatively large errors in the positions of the atoms at the terminus of side
chain; such atoms often have a functional importance, particularly when located near the
active site.

Model assessment

Assessment of homology models without reference to the true target structure is usually
performed with two methods: statistical potentials or physics-based energy calculations.
Both methods produce an estimate of the energy (or an energy-like analog) for the model or
models being assessed; independent criteria are needed to determine acceptable cutoffs.
Neither of the two methods correlates exceptionally well with true structural accuracy,
especially on protein types underrepresented in the PDB, such as membrane proteins.

Statistical potentials are empirical methods based on observed residue-residue contact
frequencies among proteins of known structure in the PDB. They assign a probability or
energy score to each possible pairwise interaction between amino acids and combine these
pairwise interaction scores into a single score for the entire model. Some such methods can
also produce a residue-by-residue assessment that identifies poorly scoring regions within
the model, though the model may have a reasonable score overall. These methods
emphasize the hydrophobic core and solvent-exposed polar amino acids often present in
globular proteins. Examples of popular statistical potentials include Prosa and DOPE.

MO]

Statistical potentials are more computationally efficient than energy calculations.

Physics-based energy calculations aim to capture the interatomic interactions that are
physically responsible for protein stability in solution, especially van der Waals and
electrostatic interactions. These calculations are performed using a molecular mechanics
force field; proteins are normally too large even for semi-empirical quantum
mechanics-based calculations. The use of these methods is based on the energy landscape
hypothesis of protein folding, which predicts that a protein's native state is also its energy
minimum. Such methods usually employ implicit solvation, which provides a continuous
approximation of a solvent bath for a single protein molecule without necessitating the
explicit representation of individual solvent molecules. A force field specifically constructed
for model assessment is known as the Effective Force Field (EFF) and is based on atomic
parameters from CHARMM. [19]

A very extensive model validation report can be obtained using the Radboud Universiteit
Nijmegen [ ] "What Check" software which is one option of the Radboud Universiteit
Nijmegen "What If software package; it produces a many page document with extensive
analyses of nearly 200 scientific and administrative aspects of the model. "What Check" is
available as a free server ; it can also be used to validate experimentally determined

Homology modeling 49

structures of macromolecules.

One newer method for model assessment relies on machine learning techniques such as
neural nets, which may be trained to assess the structure directly or to form a consensus
among multiple statistical and energy-based methods. Very recent results using support
vector machine regression on a jury of more traditional assessment methods outperformed

roil

common statistical, energy-based, and machine learning methods.

Structural comparison methods

The assessment of homology models' accuracy is straightforward when the experimental
structure is known. The most common method of comparing two protein structures uses the
root-mean-square deviation (RMSD) metric to measure the mean distance between the
corresponding atoms in the two structures after they have been superimposed. However,
RMSD does underestimate the accuracy of models in which the core is essentially correctly
modeled, but some flexible loop regions are inaccurate. A method introduced for the
modeling assessment experiment CASP is known as the global distance test (GDT) and
measures the total number of atoms whose distance from the model to the experimental
structure lies under a certain distance cutoff. Both methods can be used for any subset
of atoms in the structure, but are often applied to only the alpha carbon or protein
backbone atoms to minimize the noise created by poorly modeled side chain rotameric

["2^1

states, which most modeling methods are not optimized to predict.

Benchmarking

Several large-scale benchmarking efforts have been made to assess the relative quality of
various current homology modeling methods. CASP is a community-wide prediction
experiment that runs every two years during the summer months and challenges prediction
teams to submit structural models for a number of sequences whose structures have
recently been solved experimentally but have not yet been published. Its partner CAFASP
has run in parallel with CASP but evaluates only models produced via fully automated
servers. Continuously running experiments that do not have prediction 'seasons' focus
mainly on benchmarking publicly available webservers. LiveBench and EVA run
continuously to assess participating servers' performance in prediction of imminently
released structures from the PDB. CASP and CAFASP serve mainly as evaluations of the
state of the art in modeling, while the continuous assessments seek to evaluate the model
quality that would be obtained by a non-expert user employing publicly available tools.

Accuracy

The accuracy of the structures generated by homology modeling is highly dependent on the
sequence identity between target and template. Above 50% sequence identity, models tend
to be reliable, with only minor errors in side chain packing and rotameric state, and an
overall RMSD between the modeled and the experimental structure falling around 1 A. This
error is comparable to the typical resolution of a structure solved by NMR. In the 30-50%
identity range, errors can be more severe and are often located in loops. Below 30%
identity, serious errors occur, sometimes resulting in the basic fold being mis-predicted.
This low-identity region is often referred to as the "twilight zone" within which homology
modeling is extremely difficult, and to which it is possibly less suited than fold recognition
methods. [24]

Homology modeling 50

At high sequence identities, the primary source of error in homology modeling derives from
the choice of the template or templates on which the model is based, while lower identities
exhibit serious errors in sequence alignment that inhibit the production of high-quality
models. It has been suggested that the major impediment to quality model production is
inadequacies in sequence alignment, since "optimal" structural alignments between two
proteins of known structure can be used as input to current modeling methods to produce
quite accurate reproductions of the original experimental structure. ^

Attempts have been made to improve the accuracy of homology models built with existing
methods by subjecting them to molecular dynamics simulation in an effort to improve their
RMSD to the experimental structure. However, current force field parameterizations may
not be sufficiently accurate for this task, since homology models used as starting structures
for molecular dynamics tend to produce slightly worse structures. Slight improvements
have been observed in cases where significant restraints were used during the
simulation. ]

Sources of error

The two most common and large-scale sources of error in homology modeling are poor
template selection and inaccuracies in target-template sequence alignment.
Controlling for these two factors by using a structural alignment, or a sequence alignment
produced on the basis of comparing two solved structures, dramatically reduces the errors
in final models; these "gold standard" alignments can be used as input to current modeling

[■951

methods to produce quite accurate reproductions of the original experimental structure.
Results from the most recent CASP experiment suggest that "consensus" methods
collecting the results of multiple fold recognition and multiple alignment searches increase
the likelihood of identifying the correct template; similarly, the use of multiple templates in
the model-building step may be less optimal than the use of the single correct template but
more optimal than the use of a single suboptimal one. Alignment errors may be
minimized by the use of a multiple alignment even if only one template is used, and by the
iterative refinement of local regions of low similarity. A lesser source of model errors

are errors in the template structure. The http://swift.cmbi.ru.nl/gv/pdbreport/ PDBREPORT
database lists several million, mostly very small but occasionally dramatic, errors in
experimental (template) structures that have been deposited in the PDB.

Serious local errors can arise in homology models where an insertion or deletion mutation
or a gap in a solved structure result in a region of target sequence for which there is no
corresponding template. This problem can be minimized by the use of multiple templates,
but the method is complicated by the templates' differing local structures around the gap
and by the likelihood that a missing region in one experimental structure is also missing in
other structures of the same protein family. Missing regions are most common in loops
where high local flexibility increases the difficulty of resolving the region by
structure-determination methods. Although some guidance is provided even with a single
template by the positioning of the ends of the missing region, the longer the gap, the more
difficult it is to model. Loops of up to about 9 residues can be modeled with moderate
accuracy in some cases if the local alignment is correct. Larger regions are often modeled
individually using ab initio structure prediction techniques, although this approach has met
with only isolated success.

Homology modeling 51

The rotameric states of side chains and their internal packing arrangement also present
difficulties in homology modeling, even in targets for which the backbone structure is
relatively easy to predict. This is partly due to the fact that many side chains in crystal
structures are not in their "optimal" rotameric state as a result of energetic factors in the
hydrophobic core and in the packing of the individual molecules in a protein crystal. One
method of addressing this problem requires searching a rotameric library to identify locally
low-energy combinations of packing states. It has been suggested that a major reason
that homology modeling so difficult when target-template sequence identity lies below 30%
is that such proteins have broadly similar folds but widely divergent side chain packing
arrangements.

Utility

Uses of the structural models include protein-protein interaction prediction, protein-protein
docking, molecular docking, and functional annotation of genes identified in an organism's
genome. Even low-accuracy homology models can be useful for these purposes, because
their inaccuracies tend to be located in the loops on the protein surface, which are normally
more variable even between closely related proteins. The functional regions of the protein,
especially its active site, tend to be more highly conserved and thus more accurately
modeled. [9]

Homology models can also be used to identify subtle differences between related proteins
that have not all been solved structurally. For example, the method was used to identify
cation binding sites on the Na + /K + ATPase and to propose hypotheses about different

TOO]

ATPases' binding affinity. Used in conjunction with molecular dynamics simulations,
homology models can also generate hypotheses about the kinetics and dynamics of a
protein, as in studies of the ion selectivity of a potassium channel. Large-scale
automated modeling of all identified protein-coding regions in a genome has been
attempted for the yeast Saccharomyces cerevisiae, resulting in nearly 1000 quality models
for proteins whose structures had not yet been determined at the time of the study, and
identifying novel relationships between 236 yeast proteins and other previously solved

T351

structures.

See also

• Protein structure prediction

• Protein structure prediction software

• Protein threading

References

[1] Marti-Renom MA, Stuart AC, Fiser A, Sanchez R, Melo F, Sali A. (2000). Comparative protein structure

modeling of genes and genomes. Annu Rev Biophys Biomol Struct 29: 291-325.
[2] Chung SY, Subbiah S. (1996.) A structural explanation for the twilight zone of protein seguence homology.

Structure 4: 1123-27.
[3] Williamson AR. (2000). Creating a structural genomics consortium. Nat Struct Biol 7 Sl(lls):953.
[4] Venclovas C, Margelevicius M. (2005). Comparative modeling in CASP6 using consensus approach to template

selection, seguence-structure alignment, and structure assessment. Proteins 61(S7):99-105.
[5] Dalai S, Balasubramanian S, Regan L. (1997). Transmuting alpha helices and beta sheets. Fold Des 2(5):R71-9.
[6] Dalai S, Balasubramanian S, Regan L. (1997). Protein alchemy: changing beta-sheet into alpha-helix. Nat

Struct Biol 4(7):548-52.

Homology modeling 52

[7] Muckstein U, Hofacker IL, Stadler PF. (2002). Stochastic pairwise alignments. Bioinformatics 18 Suppl

2:S153-60.
[8] Rychlewski L, Zhang B, Godzik A. (1998). Fold and function predictions for Mycoplasma genitalium proteins.

Fold Des 3(4):229-38.
[9] Baker D, Sali A. (2001). Protein structure prediction and structural genomics. Science 294(5540):93-96.
[10] Greer J. (1981). Comparative model-building of the mammalian serine proteases 153(4):1027-42.
[11] Wallner B, Elofsson A. (2005). All are not egual: A benchmark of different homology modeling programs.

Protein Science 14:1315-1327.
[12] Levitt M. (1992). Accurate modeling of protein conformation by automatic segment matching. J Mol Biol

226(2): 507-33.
[13] Sali A, Blundell TL. (1993). Comparative protein modelling by satisfaction of spatial restraints. J Mol Biol

234(3):779-815.
[14] Fiser A, Sali A. (2003). ModLoop: automated modeling of loops in protein structures. Bioinformatics

19(18):2500-1.
[15] Topf M, Baker ML, Marti-Renom MA, Chiu W, Sali A. (2006). Refinement of protein structures by iterative

comparative modeling and CryoEM density fitting. J Mol Biol 357(5):1655-68.
[16] John B, Sali A. (2003). Comparative protein structure modeling by iterative alignment, model building and

model assessment. Nucleic Acids Res 31(14):3982-92.
[17] Ursula Pieper, Narayanan Eswar, Hannes Braberg, M.S. Madhusudhan, Fred Davis, Ashley C. Stuart, Nebojsa

Mirkovic, Andrea Rossi, Marc A. Marti-Renom, Andras Fiser, Ben Webb, Daniel Greenblatt, Conrad Huang, Tom

Ferrin, Andrej Sali. MODBASE, a database of annotated comparative protein structure models, and associated

resources. Nucleic Acids Res 32, D217-D222, 2004.
[18] Sippl MJ. (1993). Recognition of Errors in Three-Dimensional Structures of Proteins. Proteins 17:355-62.
[19] Lazaridis T. and Karplus M. 1999a. Discrimination of the native from misfolded protein models with an

energy function including implicit solvation. J. Mol. Biol. 288: 477-487
[20] http://swift.cmbi.ru.nl/gv/whatcheck/
[21] Eramian D, Shen M, Devos D, Melo F, Sali A, Marti-Renom MA. (2006). A composite score for predicting

errors in protein structure models. Protein Science 15:1653-1666.
[22] Zemla A. (2003). LGA - A Method for Finding 3-D Similarities in Protein Structures. Nucleic Acids Research,

31(13):3370-3374.
[23] Mount DM. (2004). Bioinformatics: Sequence and Genome Analysis 2nd ed. Cold Spring Harbor Laboratory

Press: Cold Spring Harbor, NY.
[24] Blake JD, Cohen FE. (2001). Pairwise sequence alignment below the twilight zone. J Mol Biol 307(2):721-35.
[25] Zhang Y and Skolnick J. (2005). The protein structure prediction problem could be solved using the current

PDB library. Proc. Natl. Acad. Sci. USA 102(4):1029-34.
[26] Koehl P, Levitt M. (1999). A brighter future for protein structure prediction. Nat Struct Biol 6(2):108-11.
[27] Flohil JA, Vriend G, Berendsen HJ. (2002). Completion and refinement of 3-D homology models with restricted

molecular dynamics: application to targets 47, 58, and 111 in the CASP modeling competition and posterior

analysis. Proteins 48(4):593-604.
[28] Ginalski K. (2006). Comparative modeling for protein structure prediction. Curr Opin Struct Biol 16(2):172-7.
[29] Kryshtafovych A, Venclovas C, Fidelis K, Moult J. (2005). Progress over the first decade of CASP experiments.

Proteins 61 (S7):225-36.
[30] Vasquez M. (1996). Modeling side-chain conformation. Curr Opin Struct Biol 6(2):217-21.
[31] Wilson C, Gregoret LM, Agard DA. (1993). Modeling side-chain conformation for homologous proteins using

an energy-based rotamer search. J Mol Biol 229(4):996-1006.
[32] Gopal S, Schroeder M, Pieper U, Sczyrba A, Aytekin-Kurban G, Bekiranov S, Fajardo JE, Eswar N, Sanchez R,

Sali A, Gaasterland T. (2001). Homology-based annotation yields 1,042 new candidate genes in the Drosophila

melanogaster genome. Nat Genet 27(3):337-40.
[33] Ogawa H, Toyoshima C. (2002). Homology modeling of the cation binding sites of Na+K+-ATPase. Proc Natl

Acad Sci USA 99(25):15977-15982
[34] Capener CE, Shrivastava IH, Ranatunga KM, Forrest LR, Smith GR, Sansom MSP. (2000). Homology

Modeling and Molecular Dynamics Simulation Studies of an Inward Rectifier Potassium Channel. Biophys J

78(6):2929-2942
[35] Sanchez R, Sali A. (1998). Large-scale protein structure modeling of the Saccharomyces cerevisiae genome.

Proc Natl Acad Sci USA 95(23):13597-13602.

Loop modeling 53

Loop modeling

Loop modeling is a problem in protein structure prediction requiring the prediction of the
conformations of loop regions in proteins without the use of a structural template. The
problem arises often in homology modeling, where the tertiary structure of an amino acid
sequence is predicted based on a sequence alignment to a template, or a second sequence
whose structure is known. Because loops have highly variable sequences even within a
given structural motif or protein fold, they often correspond to unaligned regions in
sequence alignments; they also tend to be located at the solvent-exposed surface of
globular proteins and thus are more conformationally flexible. Consequently, they often
cannot be modeled using standard homology modeling techniques. More constrained
versions of loop modeling are also used in the data fitting stages of solving a protein
structure by X-ray crystallography, because loops can correspond to regions of low electron
density and are therefore difficult to resolve.

Regions of a structural model that were predicted by loop modeling tend to be much less
accurate than regions that were predicted using template-based techniques. The extent of
the inaccuracy increases with the number of amino acids in the loop. The loop amino acids'
side chains dihedral angles are often approximated from a rotamer library, but can worsen
the inaccuracy of side chain packing in the overall model. Andrej Sali's homology modeling
suite MODELLER includes a facility explicitly designed for loop modeling by a satisfaction
of spatial restraints method.

Short loops

In general, the most accurate predictions are for loops of fewer than 8 amino acids.
Extremely short loops of three residues can be determined from geometry alone, provided
that the bond lengths and bond angles are specified. Slightly longer loops are often
determined from a "spare parts" approach, in which loops of similar length are taken from
known crystal structures and adapted to the geometry of the flanking segments. In some
methods, the bond lengths and angles of the loop region are allowed to vary, in order to
obtain a better fit; in other cases, the constraints of the flanking segments may be varied to
find more "protein-like" loop conformations. The accuracy of such short loops may be
almost as accurate as that of the homology model upon which it is based. It should also be
considered that the loops in proteins may not be well-structured and therefore have no one
conformation that could be predicted; NMR experiments indicate that solvent-exposed
loops are "floppy" and adopt many conformations, while the loop conformations seen by
X-ray crystallography may merely reflect crystal packing interactions, or the stabilizing
influence of crystallization co-solvents.

Loop modeling 54

References

• Mount DM. (2004). Bioinformatics: Sequence and Genome Analysis 2nd ed. Cold Spring
Harbor Laboratory Press: Cold Spring Harbor, NY.

• Chung SY, Subbiah S. (1996.) A structural explanation for the twilight zone of protein
sequence homology. Structure 4: 1123-27.

External links

n 1

• MODLOOP L , public server for access to MODELLER'S loop modeling facility

References

[ 1 ] http ://modbase. compbio.ucsf. edu/modloop

MODELLER

MODELLER is a computer program used in producing homology models of protein tertiary
structures as well as quaternary structures (rarer). It implements a technique inspired by
nuclear magnetic resonance known as satisfaction of spatial restraints, by which a set of
geometrical criteria are used to create a probability density function for the location of
each atom in the protein. The method relies on an input sequence alignment between the
target amino acid sequence to be modeled and a template protein whose structure has been
solved.

The program also incorporates limited functionality for ab initio structure prediction of loop
regions of proteins, which are often highly variable even among homologous proteins and
therefore difficult to predict by homology modeling.

MODELLER was originally written and is currently maintained by Andrej Sali at the
University of California, San Francisco. Although it is freely available for academic use,
graphical user interfaces and commercial versions are distributed by Accelrys.

External links

• MODELLER [1]

References

• Sali A, Blundell TL. (1993). Comparative protein modelling by satisfaction of spatial
restraints. J. Mol. Biol. 234, 779-815.

• Marti-Renom MA, Stuart A, Fiser A, Sanchez R, Melo F, Sali A. (2000). Comparative
protein structure modeling of genes and genomes. Annu. Rev. Biophys. Biomol. Struct.
29, 291-325.

• Fiser A, Sali A. (2003) Modeller: generation and refinement of homology-based protein
structure models. Methods Enzymol. 374:461-91

MODELLER 55

References

[1] http://salilab.org/modeller/

Molecular models of DNA

Molecular models of DNA structures are representations of the molecular geometry and
topology of Deoxyribonucleic acid (DNA) molecules using one of several means, such as:
closely packed spheres (CPK models) made of plastic, metal wires for 'skeletal models',
graphic computations and animations by computers, artistic rendering, and so on, with the
aim of simplifying and presenting the essential, physical and chemical, properties of DNA
molecular structures either in vivo or in vitro. Computer molecular models also allow
animations and molecular dynamics simulations that are very important for understanding
how DNA functions in vivo. Thus, an old standing dynamic problem is how DNA
"self-replication" takes place in living cells that should involve transient uncoiling of
supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongated
biopolymer molecules called "fibers" or chains (that are made of repeating nucleotide units
of four basic types, attached to deoxyribose and phosphate groups), its molecular structure
in vivo undergoes dynamic configuration changes that involve dynamically attached water
molecules and ions. Supercoiling, packing with histones in chromosome structures, and
other such supramolecular aspects also involve in vivo DNA topology which is even more
complex than DNA molecular geometry, thus turning molecular modeling of DNA into an
especially challenging problem for both molecular biologists and biotechnologists. Like
other large molecules and biopolymers, DNA often exists in multiple stable geometries (that
is, it exhibits conformational isomerism) and configurational, quantum states which are
close to each other in energy on the potential energy surface of the DNA molecule. Such
geometries can also be computed, at least in principle, by employing ab initio quantum
chemistry methods that have high accuracy for small molecules. Such quantum geometries
define an important class of ab initio molecular models of DNA whose exploration has
barely started.

In an interesting twist of roles, the DNA molecule itself was proposed to
be utilized for quantum computing. Both DNA nanostructures as well as
DNA 'computing' biochips have been built (see biochip image at right).

The more advanced, computer-based molecular models of DNA involve
molecular dynamics simulations as well as quantum mechanical
computations of vibro-rotations, delocalized molecular orbitals (MOs),
electric dipole moments, hydrogen-bonding, and so on.

DNA computing
biochip :3D

Molecular models of DNA

Importance

From the very early stages of structural studies of DNA by X-ray
diffraction and biochemical means, molecular models such as the
Watson-Crick double-helix model were successfully employed to solve the
'puzzle' of DNA structure, and also find how the latter relates to its key
functions in living cells. The first high quality X-ray diffraction patterns
of A-DNA were reported by Rosalind Franklin and Raymond Gosling in
1953 . The first calculations of the Fourier transform of an atomic helix
were reported one year earlier by Cochran, Crick and Vand , and were
followed in 1953 by the computation of the Fourier transform of a
coiled-coil by Crick [ ^ . The first reports of a double-helix molecular
model of B-DNA structure were made by Watson and Crick in 1953 .

Last-but-not-least, Maurice F. Wilkins, A. Stokes and H.R. Wilson,
reported the first X-ray patterns of in vivo B-DNA in partially oriented
salmon sperm heads [ ] . The development of the first correct
double-helix molecular model of DNA by Crick and Watson may not have

been possible without the biochemical evidence for the nucleotide base-pairing ([A— T];

[C-G]), or Chargaff's rules [7] [8] [9] [10] [11] [12] .

Spinning DNA
generic model.

Examples of DNA molecular models

Animated molecular models allow one to visually explore the three-dimensional (3D)
structure of DNA. The first DNA model is a space-filling, or CPK, model of the DNA
double-helix whereas the third is an animated wire, or skeletal type, molecular model of
DNA. The last two DNA molecular models in this series depict quadruplex DNA that
may be involved in certain cancers . The last figure on this panel is a molecular

model of hydrogen bonds between water molecules in ice that are similar to those found in
DNA.

Molecular models of DNA

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• Spacefilling model or CPK model - a molecule is represented by overlapping spheres
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Images for DNA Structure Determination from X-Ray
Patterns

The following images illustrate both the principles and the main steps involved in
generating structural information from X-ray diffraction studies of oriented DNA fibers with
the help of molecular models of DNA that are combined with crystallographic and
mathematical analysis of the X-ray patterns. From left to right the gallery of images shows:

• First row.

• 1. Constructive X-ray interference, or diffraction, following Bragg's Law of X-ray
"reflection by the crystal planes";

• 2. A comparison of A-DNA (crystalline) and highly hydrated B-DNA (paracrystalline) X-ray
diffraction, and respectively, X-ray scattering patterns (courtesy of Dr. Herbert R. Wilson,
FRS- see refs. list);

• 3. Purified DNA precipitated in a water jug;

• 4. The major steps involved in DNA structure determination by X-ray crystallography
showing the important role played by molecular models of DNA structure in this iterative,
structure-determination process;

• Second row.

Molecular models of DNA

• 5. Photo of a modern X-ray diffractometer employed for recording X-ray patterns of DNA
with major components: X-ray source, goniometer, sample holder, X-ray detector and/or
plate holder;

• 6. Illustrated animation of an X-ray goniometer;

• 7. X-ray detector at the SLAC synchrotron facility;

• 8. Neutron scattering facility at ISIS in UK;

• Third and fourth rows: Molecular models of DNA structure at various scales; figure
#11 is an actual electron micrograph of a DNA fiber bundle, presumably of a single
bacterial chromosome loop.

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Paracrystalline lattice models of B-DNA structures

A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant
amounts (e.g., larger than a few percent) of partial disordering of molecular
arranegements. Limiting cases of the paracrystal model are nanostructures, such as
glasses, liquids, etc., that may possess only local ordering and no global order. Liquid
crystals also have paracrystalline rather than crystalline structures.

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Molecular models of DNA

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which
is a dynamic one in spite of the relatively rigid DNA double-helix stabilized by parallel
hydrogen bonds between the nucleotide base-pairs in the two complementary, helical DNA
chains (see figures). For simplicity most DNA molecular models ommit both water and ions
dynamically bound to B-DNA, and are thus less useful for understanding the dynamic
behaviors of B-DNA in vivo. The physical and mathematical analysis of X-ray and

spectroscopic data for paracrystalline B-DNA is therefore much more complicated than that
of crystalline, A-DNA X-ray diffraction patterns. The paracrystal model is also important for
DNA technological applications such as DNA nanotechnology. Novel techniques that
combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now
also being developed (see, for example, "Application of X-ray microscopy in the analysis of

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living hydrated cells" ).

Genomic and Biotechnology Applications of DNA molecular
modeling

The following gallery of images illustrates various uses of DNA molecular modeling in
Genomics and Biotechnology research applications from DNA repair to PCR and DNA
nanostructures; each slide contains its own explanation and/or details. The first slide
presents an overview of DNA applications, including DNA molecular models, with emphasis
on Genomics and Biotechnology.

Gallery: DNA Molecular modeling applications

Molecular models of DNA

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Databases for DNA molecular models and sequences

X-ray diffraction

• NDB ID: UD0017 Database [13]

• X-ray Atlas -database [19]

• PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl.

DNA) crystals

[20]

• Structure factors dowloadable files in CIF format

Molecular models of DNA

Neutron scattering

• ISIS neutron source

• ISIS pulsed neutron source:A world centre for science with neutrons & muons at
Harwell, near Oxford, UK. [22]

X-ray microscopy

• Application of X-ray microscopy in the analysis of living hydrated cells

[18]

Electron microscopy

• DNA under electron microscope

[23]

Atomic Force Microscopy (AFM)

Two-dimensional DNA junction arrays have been visualized by Atomic Force Microscopy
(AFM) . Other imaging resources for AFM/Scanning probe microscopy(SPM) can be
freely accessed at:

• How SPM Works [25]

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [26]

Gallery of AFM Images

Molecular models of DNA

Mass spectrometry— Maldi informatics

Data acquisition

I List of peak
I masses

Peak detection

_ 5 J List of peak
^n intensities

Genotype,
mutations, etc.

Spectroscopy

• Vibrational circular dichroism (VCD)

• FT-NMR [27] [28]

• NMR Atlas-database [29]

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data

[30]

• NMR constraints files for NAs in PDB format [31]
NMR microscopy 1 '
Microwave spectroscopy
FT-IR

FT . NIR [33] [34] [35]

Spectral Hyperspectral, and Chemical imaging) [36] [37] [38] [39] [40] [41] [42] .
Raman spectroscopy/microscopy and CARS

Fluorescence correlation spectroscopy' 451 [46] [47] [48] [49] [50] [51] [52] , Fluorescence
cross-correlation spectroscopy and FRET

Confocal microscopy

[56]

Molecular models of DNA

Gallery: CARS (Raman spectroscopy), Fluorescence confocal
microscopy, and Hyperspectral imaging

Molecular models of DNA

Genomic and structural databases

• CBS Genome Atlas Database — contains examples of base skews.

• The Z curve database of genomes — a 3-dimensional visualization and analysis tool of
genomes [59][60] .

• DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids
molecular structure models in PDB and CIF formats

Notes

[I] Franklin, R.E. and Gosling, R.G. recd.6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium
Thymonucleate Fibres I. The Influence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium
Thymonucleate Fibres II. The Cylindrically Symmetrical Patterson Function.

[2] Cochran, W., Crick, F.H.C. and Vand V. 1952. The Structure of Synthetic Polypeptides. 1. The Transform of

Atoms on a Helix. Acta Cryst. 5(5):581-586.
[3] Crick, F.H.C. 1953a. The Fourier Transform of a Coiled-Coil., Acta Crystallographica 6(8-9):685-689.
[4] Watson, J.D; Crick F.H.C. 1953a. Molecular Structure of Nucleic Acids- A Structure for Deoxyribose Nucleic

Acid., Nature 171(4356):737-738.
[5] Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Qunatitative Biology

18:123-131.
[6] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R (1953).

"http://www.nature.com/nature/dna50/wilkins.pdflMolecular Structure of Deoxypentose Nucleic Acids" (PDF).

Nature 111. 738-740. doi: 10.1038/171738a0 (http://dx.doi.org/10.1038/171738a0). PMID 13054693. http:/

/www. nature.com/nature/dna50/wilkins.pdf.
[7] Elson D, Chargaff E (1952). "On the deoxyribonucleic acid content of sea urchin gametes". Experientia 8 (4):

143-145.
[8] Chargaff E, Lipshitz R, Green C (1952). "Composition of the deoxypentose nucleic acids of four genera of

sea-urchin". J Biol Chem 195 (1): 155-160. PMID 14938364.
[9] Chargaff E, Lipshitz R, Green C, Hodes ME (1951). "The composition of the deoxyribonucleic acid of salmon

sperm". J Biol Chem 192 (1): 223-230. PMID 14917668.
[10] Chargaff E (1951). "Some recent studies on the composition and structure of nucleic acids". J Cell Physiol

Suppl 38 (Suppl).

[II] Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E (1950). "The separation and estimation of
ribonucleotides in minute guantities". J Biol Chem 186 (1): 37-50. PMID 14778802.

[12] Chargaff E (1950). "Chemical specificity of nucleic acids and mechanism of their enzymatic degradation".

Experientia 6 (6): 201-209.
[13] http ://ndbserver. rutgers. edu/atlas/xray/structures/U/udOO 1 7/ud00 1 7. html
[14] http ://www. phy. cam. ac. uk/research/bss/molbiophysics . php
[15] http://planetphysics.org/encyclopedia/TheoreticalBiophysics.html
[16] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam - New

York, 1962.
[17] Baianu, I.C. (1978). "X-ray scattering by partially disordered membrane systems.". Acta Cryst., A34 (5):

751-753. doi: 10.1107/S0567739478001540 (http://dx.doi.org/10.1107/S0567739478001540).
[18] http://www.ncbi.nlm.nih. gov/ entrez/guery.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&

list uids=12379938
[19] http ://ndbserver. rutgers. edu/atlas/xray/index. html
[20] http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-biol/

Molecular models of DNA 68

[21] http://ndbserver.rutgers.edu/ftp/NDB/structure-factors/

[22] http://www.isis.rl.ac.uk/

[23] http://www.fidelitysystems.com/Unlinked_DNA.html

[24] Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA

Holliday Junction Arrays Visualized by Atomic Force Microscopy". Journal of the American Chemical Society

121 (23): 5437-5443. doi: 10.1021/ja9900398 (http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863

(http://worldcat.org/issn/0002-7863).
[25] http://www.parkafm.com/New_html/resources/01general.php
[26] http://www.rhk-tech.com/results/showcase.php

[27] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants
[28] (http://www.spectroscopynow.com/FCKeditor/UserFiles/File/specNOW/HTML files/

General_Karplus_Calculator.htm) Another Javascript-like NMR coupling constant to dihedral
[29] http://ndbserver.rutgers.edu/atlas/nmr/index.html
[30] http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-nmr-mmcif/
[31] http://ndbserver.rutgers.edu/ftp/NDB/nmr-restraints/

[32] Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.
[33] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.e. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[34] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[35] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.
[36] http://www.imaging.net/chemical-imaging/Chemical imaging
[37] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee

and L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical

Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.
[38] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy.,

Microchimica Acta, 104, (1-6) January 1991, doi: 10.1007/BF01245536
[39] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.e. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[40] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[41] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical

Industry, G.I.T. Laboratory Journal Europe, No. 1-2, 2007.
[42] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology. (June 2004)., I. C.

Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047)
[43] Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/ImagingMicroscopy04.pdf)
[44] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for

Biology and Medicine., doi:10.1146/annurev.anchem. 1.031207. 112754 Annual Review of Analytical Chemistry,

1: 883-909.
[45] Eigen, M., Rigler, M. Sorting single molecules: application to diagnostics and evolutionary

biotechnology, (1994) Proc. Natl. Acad. Sci. USA, 91,5740-5747.
[46] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in

biotechnology,(1995) J. Biotechnol., 41,177-186.
[47] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation

spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.
[48] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al.,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[49] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based

amplification combined with fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.
[50] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in

giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.

Molecular models of DNA 69

[51] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by

fluorescence correlation spectroscopy with one- and two-photon excitation. Biophysical Journal,

77(10):2251-2265.
[52] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.e. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[53] FRET description (http://dwb.unl.edu/Teacher/NSF/C08/C08Links/pps99.cryst.bbk.ac.uk/projects/

gmocz/fret.htm)
[54] doi:10.1016/S0959-440X(00)00190-l (http://dx.doi.org/10. 1016/S0959-440X(00)00190-l)Recent

advances in FRET: distance determination in protein-DNA complexes. Current Opinion in Structural Biology

2001, 11(2), 201-207
[55] http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction
[56] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary

biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.
[57] http://www.cbs.dtu.dk/services/GenomeAtlas/
[58] Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic results

and DNA seguence data". Bioinformatics 20: 3682-3686.
[59] http://tubic.tju.edu.cn/zcurve/
[60] Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome seguences".

Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041
[61] http://ndbserver.rutgers.edu/ftp/NDB/models/

References

Applications of Novel Techniques to Health Foods, Medical and Agricultural

Biotechnology. (June 2004) I. C. Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin.,

q-bio/0406047.

F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen

(1824), article 14.

Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and

Sons, Ltd., vols. 1 and 2., 1966., 2024 pages.

Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II. , San Franscisco:

W.H. Freeman and Co. 1980. 1,800 pages.

Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics

and evolutionary biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.

Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology,

Marcel-Dekker, New York, NY.

Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by

fluorescence correlation spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.

Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical

Imaging and Fluorescence Microspectroscopy.2004. I. C. Baianu, D. Costescu, N. E.

Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004).

Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley

& Sons, Inc., 1995, ISBN: 0-471-58651-X., 1361 pages.

Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge

University Press. ISBN 0-521-48391-3.

Watson, James D. and Francis H.C. Crick. A structure for Deoxyribose Nucleic Acid

(http://www.nature.com/nature/dna50/watsoncrick.pdf) (PDF). Nature 111, 737-738,

25 April 1953.

Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A.

Benjamin, Inc. 1965., 494 pages.

Molecular models of DNA 70

• Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science,
Inc. 2000.

• Herbert R. Wilson, FRS. Diffraction of X-rays by proteins. Nucleic Acids and Viruses.,
London: Edward Arnold (Publishers) Ltd. 1966.

• Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane, Chicester,
Toronto, Singapore: J. Wiley & Sons. 1986., 292 pages.

• Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A
Self-Assembling Molecular-Scale Memory Device". Protein Engineering 1 (4): 295-300.
ISSN 0269-2139 (http://worldcat.org/issn/0269-2139). Link (http://peds.

oxf ordj ournals . org/cgi/content/abstract/ 1/4/295)

• Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson,
Deborah Kuchnir & Winfree, Erik (22 December 2004). "Design and Characterization of
Programmable DNA Nanotubes". Journal of the American Chemical Society 126 (50):
16344-16352. doi: 10. 1021/ja0443191 (http://dx.doi.org/10.1021/ja0443191). ISSN
0002-7863 (http://worldcat.org/issn/0002-7863).

• Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun
(November 2003).

"http://www.sciencemag.org/cgi/content/abstract/sci;302/5649/1380|DNA-Templated
Carbon Nanotube Field-Effect Transistor". Science 302 (6549): 1380-1382. doi:
10.1126/science.l091022 (http://dx.doi.org/10.1126/science.1091022). ISSN
1095-9203 (http://worldcat.org/issn/1095-9203). http://www.sciencemag.org/cgi/
content/abstract/sci;302/5649/1380.

• Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl,
Richard A. & Seeman Nadrian C. (2006). "2D Nanoparticle Arrays Show the
Organizational Power of Robust DNA Motifs". Nano Letters 6: 1502-1504. doi:
10.1021/nl060994c (http://dx.doi.org/10.1021/nl060994c). ISSN 1530-6984 (http://
worldcat.org/issn/1530-6984).

• Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single
Molecules on DNA Nanostructures". Angewandte Chemie 46 (42): 7956-7959. doi:
10. 1002/anie. 200702767 (http://dx.doi.org/10.1002/anie.200702767). ISSN
0570-0833 (http://worldcat.org/issn/0570-0833).

• Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed
Two-Dimensional DNA Holliday Junction Arrays Visualized by Atomic Force Microscopy".
Journal of the American Chemical Society 111 (23): 5437-5443. doi: 10.1021/ja9900398
(http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863 (http://worldcat.org/issn/
0002-7863).

• Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping;
Ding, Baoquan; Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie &
Seeman, Nadrian C. (2006). "Double cohesion in structural DNA nanotechnology".
Organic and Biomolecular Chemistry 4: 3414-3419. doi: 10.1039/b605212f (http://dx.
doi.org/10.1039/b605212f).

Molecular models of DNA 71

See also

DNA

Molecular graphics

DNA structure

DNA Dynamics

X-ray scattering

Neutron scattering

Crystallography

Crystal lattices

Paracrystalline lattices/Paracrystals

2D-FT NMRI and Spectroscopy

NMR Spectroscopy

Microwave spectroscopy

Two-dimensional IR spectroscopy

Spectral imaging

Hyperspectral imaging

Chemical imaging

NMR microscopy

VCD or Vibrational circular dichroism

FRET and FCS- Fluorescence correlation spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS)

Molecular structure

Molecular geometry

Molecular topology

DNA topology

Sirius visualization software

Nanostructure

DNA nanotechnology

Imaging

Atomic force microscopy

X-ray microscopy

Liquid crystal

Glasses

QMC@Home

Sir Lawrence Bragg, FRS

Sir John Randall

James Watson

Francis Crick

Maurice Wilkins

Herbert Wilson, FRS

Alex Stokes

Molecular models of DNA 72

External links

DNA the Double Helix Game (http://nobelprize.org/educational_games/medicine/

dnadoublehelix/) From the official Nobel Prize web site

MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. wesleyan.edu:8080/

MDDNA/)

Double Helix 1953-2003 (http://www.ncbe.reading.ac.uk/DNA50/) National Centre

for Biotechnology Education

DNA under electron microscope (http://www.fidelitysystems.com/Unlinked_DNA.

html)

Ascalaph DNA (http://www.agilemolecule.com/Ascalaph/Ascalaph_DNA.html) —

Commercial software for DNA modeling

DNAlive: a web interface to compute DNA physical properties (http://mmb.pcb.ub.es/

DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and

DNA dynamics.

DiProDB: Dinucleotide Property Database (http://diprodb.fli-leibniz.de). The database

is designed to collect and analyse thermodynamic, structural and other dinucleotide

properties.

Further details of mathematical and molecular analysis of DNA structure based on X-ray

data (http://planetphysics.org/encyclopedia/

BesselFunctionsApplicationsToDiffractionByHelicalStructures.html)

Bessel functions corresponding to Fourier transforms of atomic or molecular helices.

(http://planetphysics.org/?op=getobj&from=objects&

name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures)

Application of X-ray microscopy in analysis of living hydrated cells (http://www.ncbi.

nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&

list_uids=12379938)

Characterization in nanotechnology some pdfs (http://nanocharacterization.sitesled.

com/)

overview of STM/AFM/SNOM principles with educative videos (http://www.ntmdt.ru/

SPM-Techniques/Principles/)

SPM Image Gallery - AFM STM SEM MFM NSOM and More (http://www.rhk-tech.com/

results/showcase. php)

How SPM Works (http://www.parkafm.com/New_html/resources/01general.php)

U.S. National DNA Day (http://www.genome.gov/10506367) — watch videos and

participate in real-time discusssions with scientists.

The Secret Life of DNA - DNA Music compositions (http://www.tjmitchell.com/stuart/

dna.html)

List of nucleic acid simulation software

List of nucleic acid simulation
software

This is a list of computer programs that are used for nucleic acids simulations.

Min - Optimization, MD - Molecular Dynamics, MC - Monte Carlo,

Crt - Cartesian coordinates. Int - Internal coordinates Exp - Explicit water. Imp - Implicit
water.

Lig - Ligands interactions. HA - Hardware accelerated.

Name

Abalone+

AMBEF.
[1]

View
3D

Model
Build

Min

MC Crt Int Exp

Imp

Lig

HA CommentsLicenstHomepage

DNA,

proteins,

ligands

AMBER

Force

Field

Comme,

Comma

5 £g\?e

Molecule
[1]

Sffiokrmd.

[5]

erg

CHARMM

ICM

[2]

JUMNA)
t""

[4]

+ +

CHARMM

Force

Field

Global
optimizatio

Comme.

[9]

org

Comm

»kt

[3]

Commercial

MDyna^i

[5]

Common
MD

GPL

Stockholm

University
[21]

MOE

Molecular
Operating
Environment

Comm

^clMiical

Computing

Group
[22] *

NAB
[6]

NAMD

Nucleic

Acid

Builder

NAnoscale
Molecular
Dynamics

GPL

Free

New

Jersey

University
[7]

Illinois

University
[8]

List of nucleic acid simulation software 74

See also

Molecular Modelling

Molecular graphics

Molecular mechanics

Molecular dynamics

Molecular Design software

Quantum chemistry computer programs

List of RNA structure prediction software

List of protein structure prediction software

List of software for molecular mechanics modeling

Force field

Force field implementation

References

[1] Cornell W.D., Cieplak P., Bayly C.I., Gould I.R., Merz K.M., Jr., Ferguson D.M., Spellmeyer D.C., Fox T.,

Caldwell J.W. and Kollman P. A. (1995). "A Second Generation Force Field for the Simulation of Proteins,

Nucleic Acids, and Organic Molecules". J. Am. Chem. Soc. 117: 5179-5197.
[2] Abagyan R.A., Totrov M.M. and Kuznetsov D.A. (1994). "Icm: A New Method For Protein Modeling and Design:

Applications To Docking and Structure Prediction From The Distorted Native Conformation". J. Comp. Chem.

15: 488-506.
[3] http://www.molsoft.com
[4] Lavery, R., Zakrzewska, K. and Sklenar, H. (1995). "JUMNA: junction minimisation of nucleic acids". Comp.

Phys. Commun. 91: 135-158.
[5] A.P.Lyubartsev, A.Laaksonen (2000). "MDynaMix - A scalable portable parallel MD simulation package for

arbitrary molecular mixtures". Computer Physics Communications 128: 565-589.
[6] Macke T. and Case D.A. (1998). "Modeling unusual nucleic acid structures". Molecular Modeling of Nucleic

Acids: 379-393.
[7] http://casegroup.rutgers.edu
[8] http://www.ks.uiuc.edu/Research/namd/

Folding@home

The PlayStation 3 Folding@home client displays a 3D model of the protein being simulated

Original author(s)

Vijay Pande

Developer(s)
Initial release

Stanford University / Pande Group
2000-10-01

Stable release

Windows:

6.23 (Uniprocessor)

6.23 (GPU)

Mac OS X:

6.20 (PPC-Uniprocessor)

6.20 (x86-SMP)

Linux:

6.02 (Uniprocessor)

6.02 (x64-SMP)

PlayStation 3: 1.4 [1]

/ 2008-11-26 (Windows 6.23)

Preview release

Platform

6.23beta (Windows SMP)
6.24beta (Linux x64-SMP)
6.24beta (Mac OS X x86-SMP)
/ 2009-01-20 (6.24betas)

Cross-platform

Available in
Type

English

Distributed computing

License

Proprietary [2]

Website

folding.stanford.edu

[3]

Folding@home (sometimes abbreviated as FAH or F@h) is a distributed computing (DC)
project designed to perform computationally intensive simulations of protein folding and
other molecular dynamics (MD). It was launched on October 1, 2000, and is currently
managed by the Pande Group, within Stanford University's chemistry department, under
the supervision of Professor Vijay Pande. Folding@home is the most powerful distributed
computing cluster in the world, according to Guinness, and one of the world's largest
distributed computing projects. The goal of the project is "to understand protein folding,
misfolding, and related diseases."

Folding@home

Purpose

Accurate simulations of protein folding and misfolding enable the scientific community to
better understand the development of many diseases, including sickle-cell disease
(drepanocytosis), Alzheimer's disease, Parkinson's disease, mad cow disease, cancer,
Huntington's disease, cystic fibrosis, osteogenesis imperfecta, alpha 1 -antitrypsin

T71

deficiency, and other aggregation-related diseases. More fundamentally, understanding
the process of protein folding — how biological molecules assemble themselves into a
functional state — is one of the outstanding problems of molecular biology. So far, the
Folding@home project has successfully simulated folding in the 5-10 microsecond range —
which is a far longer simulation than it was previously thought possible to model. The
Pande Group goal is to refine and improve the MD and Folding@home DC methods to the
level where it will become an essential tool for the MD research. For that goal they
collaborate with various scientific institutions. As of February 19, 2009, sixty-three
scientific research papers have been published using the project's work. A University of
Illinois at Urbana-Champaign report dated October 22, 2002 states that Folding@home
distributed simulations of protein folding are demonstrably accurate.

[ll]

Function

Folding@home does not rely on powerful
supercomputers for its data processing;
instead, the primary contributors to the
Folding@home project are many hundreds
of thousands of personal computer users
who have installed a small client program.
The client will, at the user's choice, run in
the background, utilizing otherwise unused
CPU power, or run as a Screensaver only
while the user is away. In most modern
personal computers, the CPU is rarely used
to its full capacity at all times; the
Folding@home client takes advantage of
this unused processing power.

Monitor Edit View Help

System Processes ' Resources ' File Systems

CPU History

H CPU 99.0%
Memory and Swap History

-a Memory

129.1 MiB [12.8%] of 1009.0 MiE

Swap

bytes [0.0 %] of 494.2 MiE

Network History

u1m L

. . mt |

_U_ Receiving bytes/s ^k Sending bytes/s
* Total Received □ bytes ^T Total Sent Q bytes

Folding@home when running takes advantage of

unused CPU cycles on a computer system as shown by

this computer's 99% CPU usage.

The Folding@home client periodically

connects to a server to retrieve "work

units", which are packets of data upon

which to perform calculations. Each

completed work unit is then sent back to the server. As data integrity is a major concern for

all distributed computing projects, all work units are validated through the use of a 2048 bit

digital signature.

Contributors to Folding@home may have user names used to keep track of their
contributions. Each user may be running the client on one or more CPUs; for example, a
user with two computers could run the client on both of them. Users may also contribute
under one or more team names; many different users may join together to form a team.
Contributors are assigned a score indicating the number and difficulty of completed work
units. Rankings and other statistics are posted to the Folding@home website.

Folding@home

Analysis Software

The Folding@home client utilizes modified versions of five molecular simulation programs
for calculation: TINKER, GROMACS, AMBER CPMD, and SHARPEN. [12] Where possible,
optimizations are used to speed the process of calculation. There are many variations on
these base simulation programs, each of which is given an arbitrary identifier (Core xx):

Active Cores

• GROMACS (all variants of this core use SIMD optimizations including SSE, 3DNow+ or
AltiVec, where available, unless otherwise specified)

• Gromacs (Core 78)

• Available for all Uniprocessor clients only.

• DGromacs (Core 79)

Double precision Gromacs, uses SSE2 only.
Available for all Uniprocessor clients only.
DGromacsB (Core 7b)

Nominally an update of DGromacs, but is actually based on the SMP/GPU codebases
(and is therefore a completely new core). As a result, both are still in use.
Double precision Gromacs, uses SSE2 only.
Available for all Uniprocessor clients only.
DGromacsC (Core 7c)

Double precision Gromacs, uses SSE2 only.
Available on Windows and Linux Uniprocessor clients only.
GBGromacs (Core 7a)

Gromacs with the Generalized Born implicit solvent model.
Available for all Uniprocessor clients only.
Gromacs SREM (Core 80)

Gromacs Serial Replica Exchange Method.

The Gromacs Serial Replica Exchange Method core, also known as GroST (Gromacs
Serial replica exchange with Temperatures), uses the Replica Exchange method
(also known as REMD or Replica Exchange Molecular Dynamics) in its simulations.
Available for Windows and Linux Uniprocessor clients only.
GroSimT (Core 81)

Gromacs with Simulated Tempering.

Available for Windows and Linux Uniprocessor clients only.
Gromacs 33 (Core aO)

Uses the Gromacs 3.3 codebase.
Available for all Uniprocessor clients only.
Gro-SMP (Core al)

Symmetric Multiprocessing variant, locked to four threads (but can be run on dual
core processors).

Runs only on multi-core x86 or x64 hardware, uses SSE only.
Available for all SMP clients only.
GroCVS (Core a2)

• Symmetric Multiprocessing variant with scalable numbers of threads.

Folding@home

• Runs only on multi-core x86 or x64 hardware, with four or more cores, uses SSE
only.

• Uses the Gromacs 4.0 codebase.

• Available for Linux and Mac OS X SMP clients only.

• GroGPU2 (Core 11)

• Graphics Processing Unit variant for ATI
CAL-enabled and nVidia CUDA-enabled GPUs.

• Comes in two separate versions, one each for
ATI and nVidia, but both have the same Core ID.

• GPUs do not support SIMD optimizations by
design, so none are used in this core.

• Available for GPU2 client only.

J NVIDIA GPU v2.0 rl client for

• ATI-DEV(Corel2) Windows..

• Graphics Processing Unit developmental core for ATI CAL-enabled GPUS.

• Does not support SIMD optimizations.

• Available for GPU2 client only.

• NVIDIA-DEV (Core 13)

• Graphics Processing Unit developmental core for nVidia CUDA-enabled GPUs.

• Does not support SIMD optimizations.

• Available for GPU2 client only.

• GroGPU2-MT (Core 14) [14]

• Graphics Processing Unit variant for nVidia CUDA-enabled GPUs.

• Contains additional debugging code compared to the standard Core 11.

• Does not support SIMD optimizations.

• Released March 2, 2009.

• Available for GPU2 client only.

• Gro-PS3 (Does not have a known ID number, but also called SCEARD core)

• PlayStation 3 variant.

• No SIMD optimizations, uses SPE cores for optimization.

• Available for PS 3 client only.
AMBER

• PMD (Core 82) [13]

• No optimizations.

• Available for Windows and Linux Uniprocessor clients only.

Folding@home 79

Inactive Cores

• TINKER

• Tinker core (Core 65)

• Currently inactive, as the GBGromacs core (Core 7a) performs the same tasks much
faster.

• No optimizations.

• Available for all Uniprocessor clients only.

• GROMACS

• GroGPU (Core 10)

• Graphics Processing Unit variant for ATI series lxxx GPUs.

• GPUs do not have optimizations; no SIMD optimizations needed since GPU cores are
explicitly designed for SIMD.

• Inactive as of June 6, 2008 due to end of distribution of GPU1 client units.

• Available for GPU1 client only.

• CPMD

• QMD (Core 96)

• Currently inactive, due to QMD developer graduating from Stanford University and
due to current research shifting away from Quantum MD.

• Caused controversy due to SSE2 issues involving Intel libraries and AMD

r 1 ri

processors.

• Uses SSE2 (currently only on Intel CPUs, see above).

• Available for Windows and Linux Uniprocessor clients only.

• SHARPEN [16]

• SHARPEN Core [17]

• Currently inactive, in closed beta testing before general release.

• Uses different format to standard F@H cores, as there is more than one "Work Unit"
(using the normal definition) in each work packet sent to clients.

Folding@home

Possible future additions

• ProtoMol [9]

Participation

Shortly after breaking the 200,000 active
CPU count on September 20, 2005, the
Folding@home project celebrated its fifth
anniversary on October 1, 2005.

Interest and participation in the project
has grown steadily since its launch. The
number of active devices participating in
the project increased substantially after
receiving much publicity during the
launch of their high performance clients
for both ATi graphics cards and the
PlayStation 3, and again following the
launch of the high performance client for
nVidia graphics cards.

1000 -

900 -

800 -

£ 700-

O 600 -

q! 500

2 400

,2 300 -

200 -

100 -

Folding@Home TFLOPS

I f v-y-L,. * r

„.

^A^.

"u/-^

* rw-L,

\\ ...I

V- \ ■

■

- L

3 CD
3 O
3 O
i CN
; CN

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3 O

02/01/2007 -

02/02/2007 -

02/03/2007 -

^ 02/04/2007 -

02/05/2007 -
02/06/2007 -

o
f -I
I-'-
p
'."■■"]
o

o
o
r-i

'TO

■■'
o

■■■-

D
CN

■:.7

- Total

Tflops — GPU Tflops PS3 Tflops

PC/MAC Tflops |

Folding@home computing power shown - by device type
- in TeraFLOPS as recorded semi-daily from November

2006 until September 2007. Note the large spike in total
compute power after March 22, when the PlayStation 3
client was released.

As of April 9, 2009 the peak speed of the

project overall has reached over 4.5

native PFLOPS (8.1 x86 PFLOPS [18] ) from around 400,000 active machines, and the project

has received computational results from over 3.75 million devices since it first started.

Google & Folding@home

There used to be cooperation between Folding@home and Google Labs in the form of
Google Toolbar. Google Compute supported Folding@home during its early stage — when
Folding@home had -10,000 active CPUs. At that time, a boost of 20,000 machines was
very significant. Today the project has a large number of active CPUs and the number of
new clients joining Google Compute was very low (most people opted for the
Folding@home client instead), so it was discontinued. The Google Compute clients also had
certain limits: they could only run the TINKER core and had limited naming and team
options. Folding@home is no longer supported on Google Toolbar, and even the old Google
Toolbar client will not work.

Genome@home

Folding@home absorbed the Genome@home project on March 8, 2004. The work which
was started by the Genome@home project has since been completed using the
Folding@home network (the work units without deadlines), and no new work is being
distributed by this project. All donators were encouraged to download the Folding@home
client (the F@h 4.xx client had a Genome@home option), and once the Genome@home
work was complete these clients were asked to donate their processing power to the
Folding@home project instead.

Folding@home

PetaFLOPS Milestones

Native petaFLOPS Barrier

Date Crossed

1.0

September 16, 2007

2.0

early May 2008

3.0

August 20, 2008

4.0

September 28, 2008

5.0

February 18, 2009

On September 16, 2007, the Folding@home project officially attained a sustained
performance level higher than one native petaFLOPS, becoming the first computing system
of any kind in the world to ever do so, although it had briefly peaked above one native
petaFLOPS in March 2007, receiving a large amount of main stream media coverage for

[201 T211

doing so. In early May 2008 the project attained a sustained performance level

higher than two native petaFLOPS, followed by the three and four native petaFLOPS
milestones on August 20 and September 28, 2008 respectively. On February 18, 2009,
Folding@home achieved a performance level of 5033 native TFLOPS, thereby becoming the

[221

first computing system of any kind to surpass 5 native PFLOPS , just as it was for the
other four milestones.

The Folding@home computing cluster currently operates at above 4.5 native petaFLOPS at
all times, with a large majority of the performance coming from GPU and PlayStation 3

r cr "I

clients. In comparison to this, the fastest standalone supercomputer (non-distributive
computing) in the world (as of November 2008, U.S. Department of Energy Roadrunner)
peaks at approximately 1.46 petaFLOPS/ '

Beginning in April 2009, Folding@Home began reporting performance in both "Native"
FLOPS and x86 FLOPS. [5] ("x86" FLOPS reported at a much higher mark than the "Native"
FLOPS) A detailed explanation of the difference between the two figures was given in the
FLOP section of the Folding@Home FAQ.

[24]

Results

These peer-reviewed papers (in chronological order) all use research from the

Folding@home project.

[10]

2000-2001

• M. R. Shirts and V. S. Pande. (2000). "Screen Savers of the World, Unite!". Science 290:
1903-1904. doi:10.1126/science. 290. 5498. 1903 [25] . PMID 17742054.

• Michael R. Shirts and Vijay S. Pande (2001). "Mathematical Analysis of Coupled Parallel
Simulations". Physical Review Letters 86 (22): 4983-4987.
doi:10.1103/PhysRevLett.86.4983 [26] .

• Bojan Zagrovic, Eric J. Sorin and Vijay Pande (2001). "b-Hairpin Folding Simulations in
Atomistic Detail Using an Implicit Solvent Model". Journal of Molecular Biology 313:
151-169. doi:10.1006/jmbi.2001.5033 [27] .

Folding@home 82

2002

• Stefan M. Larson, Christopher D. Snow, Michael R. Shirts, and Vijay S. Pande (2002)
"Folding@home and Genome@home: Using distributed computing to tackle previously
intractable problems in computational biology", Stefan M. Larson, Christopher D. Snow,
Michael R. Shirts, and Vijay S. Pande. To appear in Computational Genomics, Richard
Grant, editor, Horizon Press

• Bojan Zagrovic, Christopher D. Snow, Michael R. Shirts, and Vijay S. Pande. (2002).
"Simulation of Folding of a Small Alpha-helical Protein in Atomistic Detail using
Worldwide distributed Computing". Journal of Molecular Biology 323: 927-937.
doi:10.1016/S0022-2836(02)00997-X [28] .

• Bojan Zagrovic, Christopher D. Snow, Siraj Khaliq, Michael R. Shirts, and Vijay S. Pande
(2002). "Native-like Mean Structure in the Unfolded Ensemble of Small Proteins". Journal
of Molecular Biology 323: 153-164. doi:10.1016/S0022-2836(02)00888-4 [29] .

• Christopher D. Snow, Bojan Zagrovic, and Vijay S. Pande (2002). "The Trp Cage: Folding
Kinetics and Unfolded State Topology via Molecular Dynamics Simulations". Journal of
the American Chemical Society 124: 14548-14549. doi:10.1021/ja0286041 [30] .

2003

• Vijay S. Pande, Ian Baker, Jarrod Chapman, Sidney P. Elmer, Siraj Khaliq, Stefan M.
Larson, Young Min Rhee, Michael R. Shirts, Christopher D. Snow, Eric J. Sorin, Bojan
Zagrovic (2003). "Atomistic protein folding simulations on the submillisecond timescale
using worldwide distributed computing". Biopolymers 68: 91-109. doi:10.1002/bip. 10219

[31]

• Young Min Rhee & Vijay S. Pande (2003). "Multiplexed-Replica Exchange Molecular
Dynamics Method for Protein Folding Simulation". Biophysical Journal 84 (2): 775-786.

• Eric J. Sorin, Young Min Rhee, Bradley J. Nakatani & Vijay S. Pande (2003). "Insights Into
Nucleic Acid Conformational Dynamics from Massively Parallel Stochastic Simulations".
Biophysical Journal 85: 790-803.

• Bojan Zagrovic and Vijay S. Pande (2003). "Solvent Viscosity Dependence of the Folding
Rate of a Small Protein: Distributed Computing Study". Journal of Computational
Chemistry 24 (12): 1432-1436. doi:10.1002/jcc. 10297 [32] .

• Michael R. Shirts, Jed W. Pitera, William C. Swope, and Vijay S. Pande (2003). "Extremely
precise free energy calculations of amino acid side chain analogs: Comparison of
common molecular mechanics force fields for proteins". Journal of Chemical Physics 119
(11): 5740-5761. doi:10. 1063/1. 1587119 [33] .

• Michael R. Shirts, Eric Bair, Giles Hooker, and Vijay S Pande (2003). "Equilibrium Free
Energies from Nonequilibrium Measurements Using Maximum-Likelihood Methods".
Physical Review Letters 91 (14). doi:10.1103/PhysRevLett.91. 140601 [34] .

• Bojan Zagrovic & Vijay S Pande (2003). "Structural correspondence between the
alpha-helix and the random-flight chain resolves how unfolded proteins can have
native-like properties". Nature Structural Biology 10 (11): 955-961. doi:10.1038/nsb995

[35]

Folding@home 83

2004

• Eric J. Sorin, Bradley J. Nakatani, Young Min Rhee, Guha Jayachandran, V Vishal, & Vijay
S Pande (2004). "Does Native State Topology Determine the RNA Folding Mechanism?".
Journal of Molecular Biology 337: 789-757. doi:10.1016/j.jmb.2004.02.024 [36] .

• Christopher D. Snow, Linlin Qiu, Deguo Du, Feng Gai, Stephen J. Hagen, & Vijay S Pande
(2004). "Trp zipper folding kinetics by molecular dynamics and temperature-jump
spectroscopy". Proceedings of the National Academy of Sciences, USA 101 (12):
4077-4082. doi:10.1073/pnas. 0305260101 [37] .

• Young Min Rhee, Eric J. Sorin, Guha Jayachandran, Erik Lindahl, & Vijay S Pande (2004).
"Simulations of the role of water in the protein-folding mechanism". Proceedings of the
National Academy of Sciences, USA 101 (17): 6456-6461. doi:10.1073/pnas. 0307898101

[38]

• Nina Singhal, Christopher D. Snow, and Vijay S. Pande (2004). "Using path sampling to
build better Markovian state models: Predicting the folding rate and mechanism of a
tryptophan zipper beta hairpin". Journal of Chemical Physics 121: 415-425.

doi:10. 1063/1. 1738647 [39] .

• L. T. Chong, C. D. Snow, Y. M. Rhee, and V. S. Pande. (2004). "Dimerization of the p53
Oligomerization Domain: Identification of a Folding Nucleus by Molecular Dynamics
Simulations". Journal of Molecular Biology 345: 869-878. doi:10.1016/j.jmb.2004.10.083

[40]

2005

• Eric J. Sorin, Young Min Rhee, and Vijay S. Pande (2005). "Does Water Play a Structural
Role in the Folding of Small Nucleic Acids?". Biophysical Journal 88: 2516-2524.
doi:10.1529/biophysj. 104.055087 [41] .

• Eric J. Sorin and Vijay S. Pande (2005). "Exploring the Helix-Coil Transition via All-atom
Equilibrium Ensemble Simulations". Biophysical Journal 88: 2472-2493.
doi:10.1529/biophysj. 104.051938 [42] .

• Eric J. Sorin and Vijay S. Pande (2005). "Empirical Force-Field Assessment: The Interplay
Between Backbone Torsions and Noncovalent Term Scaling". Journal of Computational
Chemistry 26: 682-690. doi:10.1002/jcc. 20208 [43] .

• C. D. Snow, E. J. Sorin, Y. M. Rhee, and V. S. Pande. (2005). "How well can simulation
predict protein folding kinetics and thermodynamics?". Annual Reviews of Biophysics 34:
43-69. doi:10.1146/annurev.biophys. 34. 040204. 144447 [44] .

• Bojan Zagrovic, Jan Lipfert, Eric J. Sorin, Ian S. Millett, Wilfred F. van Gunsteren,
Sebastian Doniach & Vijay S. Pande (2005). "Unusual compactness of a polyproline type
II structure". Proceedings of the National Academy of Sciences, USA 102 (33):
11698-11703. doi:10.1073/pnas. 0409693102 [45] .

• Michael R. Shirts & Vijay S. Pande (2005). "Comparison of efficiency and bias of free
energies computed by exponential averaging, the Bennett acceptance ratio, and
thermodynamic integration". Journal of Chemical Physics 122. doi:10. 1063/1. 1873592

[46]

• Michael R. Shirts & Vijay S. Pande (2005). "Solvation free energies of amino acid side
chain analogs for common molecular mechanics water models". Journal of Chemical
Physics 122. doi:10. 1063/1. 1877132 [47] .

• Sidney Elmer, Sanghyun Park, & Vijay S. Pande (2005). "Foldamer dynamics expressed
via Markov state models. I. Explicit solvent molecular-dynamics simulations in

Folding@home 84

acetonitrile, chloroform, methanol, and water". Journal of Chemical Physics 123.
doi:10. 1063/1. 2001648 [48] .

• Sidney Elmer, Sanghyun Park, & Vijay S. Pande (2005). "Foldamer dynamics expressed
via Markov state models. II. State space decomposition". Journal of Chemical Physics
123. doi:10. 1063/1. 2008230 [49] .

• Sanghyun Park, Randall J. Radmer, Teri E. Klein, and Vijay S. Pande (2005). "A New Set
of Molecular Mechanics Parameters for Hydroxyproline and Its Use in Molecular
Dynamics Simulations of Collagen-Like Peptides". Journal of Computational Chemistry
26: 1612-1616. doi:10.1002/jcc. 20301 [50] .

• Hideaki Fujutani, Yoshiaki Tanida, Masakatsu Ito, Guha Jayachandran, Christopher D.
Snow, Michael R. Shirts, Eric J. Sorin, and Vijay S. Pande (2005). "Direct calculation of
the binding free energies of FKBP ligands using the Fujitsu BioServer massively parallel
computer". Journal of Chemical Physics 123. doi:10. 1063/1. 1999637 [51] .

• Nina Singhal and Vijay S. Pande (2005). "Error Analysis and efficient sampling in
Markovian State Models for protein folding". Journal of Chemical Physics 123.
doi:10. 1063/1. 2116947 [52] .

• Bojan Zagrovic, Guha Jayachandran, Ian S. Millett, Sebastian Doniach and Vijay S. Pande
(2005). "How large is alpha-helix in solution? Studies of the radii of gyration of helical
peptides by SAXS and MD". Journal of Chemical Physics 353: 232-241.
doi:10.1016/j.jmb.2005.08.053 [53] .

2006

• Paula Petrone and Vijay S. Pande (2006). "Can conformational change be described by
only a few normal modes?". Biophysical Journal 90: 1583-1593.
doi:10.1529/biophysj. 105. 070045 [54] .

• Eric J. Sorin, Young Min Rhee, Michael R. Shirts, and Vijay S. Pande (2006). "The
solvation interface is a determining factor in peptide conformational preferences".
Journal of Molecular Biology 356: 248-256. doi:10.1016/j.jmb.2005.11.058 [55] .

• Eric J. Sorin and Vijay S. Pande (2006). "Nanotube confinement denatures protein
helices". Journal of the American Chemical Society 128: 6316-6317.
doi:10.1021/ja060917j [56] .

• Young Min Rhee and Vijay S. Pande (2006). "On the role of chemical detail in simulating
protein folding kinetics". Chemical Physics 323: 66-77.
doi:10.1016/j.chemphys.2005.08.060 [57] .

• L.T. Chong, W. C. Swope, J. W. Pitera, and V. S. Pande (2006). "A novel approach for
computational alanine scanning: application to the p53 oligomerization domain". Journal
of Molecular Biology 357 (3): 1039-1049. doi:10.1016/j.jmb.2005.12.083 [58] .

• I. Suydam, C. D. Snow, V. S. Pande and S. G. Boxer. (2006). "Electric Fields at the Active
Site of an Enzyme: Direct Comparison of Experiment with Theory". Science 313 (5784):
200-204. doi:10.1126/science. 1127159 [59] .

• P. Kasson, N. Kelley, N. Singhal, M. Vrjlic, A. Brunger, and V. S. Pande (2006). "Ensemble
molecular dynamics yields submillisecond kinetics and intermediates of membrane
fusion". Proceedings of the National Academy of Sciences, USA 103 (32): 11916-11921.
doi:10.1073/pnas.0601597103 [60] .

• Guha Jayachandran, V. Vishal, and V. S. Pande (2006). "Folding Simulations of the Villin
Headpiece in All-Atom Detail". Journal of Chemical Physics 124. doi:10. 1063/1. 2186317

[61]

Folding@home 85

• Guha Jayachandran, M. R. Shirts, S. Park, and V. S. Pande (2006). "Parallelized Over
Parts Computation of Absolute Binding Free Energy with Docking and Molecular
Dynamics". Journal of Chemical Physics 125. doi:10. 1063/1. 2221680 [62] .

• C. Snow and V. S. Pande (2006). "Kinetic Definition of Protein Folding Transition State
Ensembles and Reaction Coordinates". Biophysical Journal 91: 14-24.
doi:10.1529/biophysj. 105. 075689 [63] .

• S. Park and V. S. Pande (2006). "A Bayesian Update Method for Adaptive Weighted
Sampling". Physical Review 74 (6). doi:10.1103/PhysRevE. 74. 066703 [64] .

• P. Kasson and V. S. Pande (2006). "Predicting structure and dynamics of loosely-ordered
protein complexes: influenza hemagglutinin fusion peptide". PSB.
doi:10.1142/9789812772435_0005 [65] . PMID 17992744.

• Erich Elsen, Mike Houston, V. Vishal, Eric Darve, Pat Hanrahan, and Vijay Pande (2006).
"N-Body simulation on GPUs". Proceedings of the 2006 ACM/IEEE conference on
Supercomputing. doi:10.1 145/1 188455.1 188649 [66] .

2007

• Guha Jayachandran, V. Vishal, Angel E. Garcia and V. S. Pande (2007). "Local structure
formation in simulations of two small proteins". Journal of Structural Biology 157 (3):
491-499. doi:10.1016/j.jsb.2006.10.001 [67] .

• Adam L Beberg and Vijay S. Pande (2007). "Storage@home: Petascale Distributed
Storage". IPDPS. doi:10.1109/IPDPS. 2007. 370672 [68] .

• J. Chodera, N. Singhal, V. S. Pande, K. Dill, and W. Swope (2007). "Automatic discovery
of metastable states for the construction of Markov models of macromolecular
conformational dynamics". Journal of Chemical Physics 126 (15). PMID 17461665.

• D. Lucent, V. Vishal, V. S. Pande (2007). "Protein folding under confinement: a role for
solvent". Proceedings of the National Academy of Sciences, USA 104 (25): 10430-10434.
doi:10.1073/pnas.0608256104 [69] .

• P. M. Kasson, A. Zomorodian, S. Park, N. Singhal, L. J. Guibas, and V. S. Pande (2007).
"Persistent voids: a new structural metric for membrane fusion". Bioinformatics .
doi:10.1093/bioinformatics/btm250 [70] .

• P. M. Kasson and V. S. Pande (2007). "Control of Membrane Fusion Mechanism by Lipid
Composition: Predictions from Ensemble Molecular Dynamics". PLoS Computational
Biology 3 (11). doi:10.1371/journal.pcbi.0030220 [71] .

• D. Ensign, P. M. Kasson, and V. S. Pande (2007). "Heterogeneity Even at the Speed Limit
of Folding: Large-scale Molecular Dynamics Study of a Fast-folding Variant of the Villin
Headpiece". Journal of Molecular Biology 374 (3): 806-816.
doi:10.1016/j.jmb.2007.09.069 [72] .

• Alex Robertson, Edgar Luttmann, Vijay S. Pande (2007). "Effects of long-range
electrostatic forces on simulated protein folding kinetics". Journal of Computational
Chemistry 29 (5): 694-700. doi:10.1002/jcc. 20828 [73] .

• Nina Singhal Hinrichs and Vijay S. Pande (2007). "Calculation of the distribution of
eigenvalues and eigenvectors in Markovian state models for molecular dynamics".
Journal of Chemical Physics 126. doi:10. 1063/1. 2740261 [74] .

Folding@home 86

2008

• Xuhui Huang, Gregory R. Bowman,and Vijay S. Pande (2008). "Convergence of folding
free energy landscapes via application of enhanced sampling methods in a distributed
computing environment". Journal of Chemical Physics 128 (20). PMID 18513049.

• Gregory R. Bowman, Xuhui Huang, Yuan Yao, Jian Sun, Gunnar Carlsson, Leonidas J.
Guibas, and Vijay S. Pande (2008). "Structural Insight into RNA Hairpin Folding
Intermediates". Journal of the American Chemical Society 130 (30): 9676-9678.
doi:10.1021/ja8032857 [75] .

• Nicholas W. Kelley, V. Vishal, Grant A. Krafft, and Vijay S. Pande. (2008). "Simulating
oligomerization at experimental concentrations and long timescales: A Markov state
model approach.". Journal of Chemical Physics 129 (21). doi:10. 1063/1. 3010881 [76] .

• Paula M. Petrone, Christopher D. Snow, Del Lucent, and Vijay S. Pande (2008).
"Side-chain recognition and gating in the ribosome exit tunnel". Proceedings of the
National Academy of Sciences, USA 105 (43): 16549-16554.
doi:10.1073/pnas.0801795105 [77] .

• Edgar Luttmann, Daniel L. Ensign, Vishal Vaidyanathan, Mike Houston, Noam Rimon,
Jeppe 01and, Guha Jayachandran, Mark Friedrichs, Vijay S. Pande (2008). "Accelerating
Molecular Dynamic Simulation on the Cell processor and PlayStation 3" . Journal of
Computational Chemistry 30 (2): 268-274. doi:10.1002/jcc. 21054 [78] .

2009

• Peter M. Kasson and Vijay S. Pande (2009). "Combining Mutual Information with
Structural Analysis to Screen for Functionally Important Residues in Influenza
Hemagglutinin". Pacific Symposium on Biocomputing 14: 492-503. PMID 19209725.

• Nicholas W. Kelley, Xuhui Huang, Stephen Tarn, Christoph Spiess, Judith Frydman and
Vijay S. Pande (2009). "The predicted structure of the headpiece of the Huntingtin
protein and its implications on Huntingtin aggregation". Journal of Molecular Biology.
doi:10.1016/j.jmb.2009.01.032 [79] .

• M. S. Friedrichs, P. Eastman, V. Vaidyanathan, M. Houston, S. LeGrand, A. L. Beberg, D.
L. Ensign, C. M. Bruns, V. S. Pande (2009). "Accelerating molecular dynamic simulation
on graphics processing units". Journal of Computational Chemistry.
doi:10.1002/jcc. 21209 [80] . PMID 19191337.

High performance platforms

Graphical processing units

On October 2, 2006, the Folding@home Windows GPU client was released to the public as a
beta test. After 9 days of processing from the Beta client the Folding@home project had
received 31 teraFLOPs of computational performance from just 450 ATI Radeon X1900
GPUs, averaging at over 7 Ox the performance of current CPU submissions, and the GPU
clients remain the most powerful clients available in terms of performance per client (as of
March 11, 2009, GPU clients accounted for over 60% of the entire project's throughput at
an approximate ratio of 9 clients per teraFLOP— nVidia clients currently lead ATI clients in
overall contribution and in performance per client). ' On April 10, 2008, the second
generation Windows GPU client was released to open beta testing, supporting ATI/AMD's
Radeon HD 2000 and HD 3000 series, and also debuting a new core (GROGPU2 - Core 11).

Folding@home 87

Inaccuracies with DirectX were cited as the main reason for the migration to the new

roil

version (the original GPU client was officially retired June 6, 2008 ), which uses
AMD/ATI's CAL. On June 17, 2008, a version of the second-generation Windows GPU client
for CUDA enabled Nvidia GPUs was also released for public beta testing. The GPU
clients proved reliable enough to be promoted out of the beta phase and were officially
released August 1, 2008. Newer GPU cores continue to be released for both CAL and
CUDA. No word has to date been given over future support for OpenCL or DirectX ll's
Compute Shaders.

While the only officially released GPU v2.0 client is for Windows, this client can be run on
Linux under Wine with NVIDIA graphics cards. The client can operate on both 32- and
64-bit Linux platforms, but in either case the 32-bit CUDA toolkit is required. This
configuration is not officially supported, though initial results have shown comparable
performance to that of the native client and no problems with the scientific results have
been found . An unofficial installation guide has been published. ]

PlayStation 3

Stanford announced in August 2006 that a

folding client was available to run on the Sony

PlayStation 3. The intent was that gamers

would be able to contribute to the project by

merely "contributing electricity", leaving their

PlayStation 3 consoles running the client while

not playing games. PS3 firmware version 1.6

(released on Thursday, March 22, 2007) allows

for Folding@home software, a 50 MB download, The PlayStation 3's Life With PlayStation client

to be used on the PS3. [5] A peak output Of the replaced the Folding@home application on 18

_ T _„ ,. , ^_ September, 2008.

project at 990 teraFLOPS was achieved on 25

March, 2007, at which time the number of

FLOPS from each PS3 as reported by Stanford fell, reducing the overall speed rating of
those machines by 50%. This had the effect of bumping down the overall project speed to
the mid 700 range and increasing the number of active PS3s required to achieve a
petaFLOPS level to around 60,000.

On April 26, 2007, Sony released a new version of Folding@home which improved folding
performance drastically, such that the updated PS3 clients produced 1500 teraFLOPS with
52,000 clients versus the previous 400 teraFLOPS by around 24,000 clients. [86] Lately, the
console accounts for around 26% of all teraFLOPS at an approximate ratio of 35V2 PS3
clients per teraFLOPS.

On December 19, 2007, Sony again updated the Folding@home client to version 1.3 to
allow users to run music stored on their hard drives while contributing. Another feature of
the 1.3 update allows users to automatically shut down their console after current work is
done or after a limited period of time (for example 3 or 4 hours). Also, the software update
added the Generalized Born implicit solvent model, so the FAH PS 3 client gained more
broad computing capabilities. Shortly afterward, 1.3.1 was released to solve a

mishandling of protocol resulting in difficulties sending and receiving Work Units due to
heavy server loads stemming from the fault.

Folding@home

On 18 September, 2008 the Folding@home client became Life With PlayStation. In addition
to the existing functionality, the application also provides the user with access to
information "channels", the first of which being the Live Channel which offers news
headlines and weather through a 3D globe. The user can rotate and zoom in to any part of
the world to access information provided by Google News and The Weather Channel,
among other sources, all running whilst folding in the background. This update also
provided more advanced simulation of protein folding and a new ranking system. ]

Multi-core processing client

As more modern CPUs are being released, the migration to
multiple cores is becoming more adopted by the public, and
the Pande Group is adding symmetric multiprocessing (SMP)
support to the Folding@home client in the hopes of
capturing the additional processing power. The SMP support
is being achieved by utilizing Message Passing Interface
protocols. In current state it is being confined inside a single
node by hard coded usage of the localhost.

On November 13, 2006, the beta SMP Folding@home clients
for x86-64 Linux and x86 Mac OS X were released. The beta
Win32 SMP Folding@home client is out as well, and a 32-bit
Linux client is currently in development.

[90]

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processor.

Folding@home teams

A typical Folding@home user, running the client on a single PC, will likely not be ranked
high on the list of contributors. However, if the user were to join a team, they would add
the points they receive to a larger collective. Teams work by using the combined score of all
their members. Thus, teams are ranked much higher than individual submitters. Rivalries
between teams create friendly competition that benefits the folding community. Many
teams publish their own stats, so members can have intra-team competitions for top
spots. Some teams offer prizes in an attempt to increase participation in the project. ^

Development

The Folding@home project does not make the project source code available to the public,
citing security and integrity concerns. At the same time, the majority of the scientific

codes used by the FAH (ex. Cosm, GROMACS, TINKER, AMBER, CPMD, BrookGPU) are
largely Open-source software or under similar licenses.

A development version of Folding@home once ran on the open source BOINC framework;
however, this version remained unreleased.

Folding@home 89

Estimated energy consumption

A PlayStation 3 has a maximum power rating of 380 watts. As Folding@home is a CPU
intensive application, it causes 100% utilization. However, according to Stanford's PS3
FAQ, "We expect the PS3 to use about 200W while running Folding@home. As of

December 27, 2008, there are 55,291 PS3s providing 1,559,000,000 MFlops of processing
power. This amounts to 28,196 MFlops/PS3, and with Stanford's estimate of 200W per PS3

T51

(for original units manufactured on the 90nm process), 140.98 MFlops/watt. This would
put the PS3 portion of Folding@home at 95th on the November 2008 Green500 list. [97] The
Cell processors used in current units of the PlayStation 3 utilize 65nm technology (lowering
power consumption to around 115W per PS3), with another upgrade to 45nm planned
(further dropping consumption to around 80W/PS3). This will further increase the power
efficiency of the contribution from PlayStation 3 units.

The total power consumption required to produce the processing power required by the
project can be estimated based upon the average FLOPS per watt. As of November 2008,
according to the Green500 list, the most efficient computer - also based on a version of the
Cell BE - runs at 536.24 MFLOPS/watt. [98] One petaFLOPS equals 1,000,000,000 MFLOPSs.
Therefore, the current Folding@home project, if it were theoretically using the most
efficient CPUs currently available, would use at least 2.8 megawatts of power per
petaFLOPS, slightly more than the world's first and only petaflop system, the Cell-based
Roadrunner which uses 2.345MW. This is equivalent to the power needed to light
approximately 40,000 standard house light bulbs (between 60 and 100 watts each), or the
equivalent of 0.5-3 electrical wind mills depending on their size.

Estimates of power usage per time period are more difficult than estimates of power usage
per processing instruction. This is because Folding@home clients are often run on
computers that would be powered-on even in the absence of the Folding@home client, and
that run other programs simultaneously. While Folding@home increases processor
utilization, and thus (usually) power consumption, the extent to which it does so is
dependent on the client processor's normal operating load, and its ability to reduce clock
speeds when presented with less-than-full utilization (a process known as dynamic
frequency scaling). Consequently, the total power usage of the Folding@home client on a
temporal basis is probably less than the figure that could be calculated by summing the
peak power consumption of each of the project's component processors.

See also

Blue Gene

Grid computing

List of distributed computing projects

Rosetta@Home

Software for molecular modeling

Molecular modeling on GPU

Folding@home 90

References

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GPU1 has been retired, GPU2 for NVIDIA release nearing". http://folding.typepad.com/news/2008/06/

gpu 1 -has-been-retired-gpu2-for-nvidia-release-nearing. html.
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GPU2 beta client for NVIDIA now released", http://folding.typepad.com/news/2008/06/

gpu2-beta-client-for-nvidia-now-released.html.
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(6.20)". http://folding.typepad.com/news/2008/08/new-clients-are-out-620.html.
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Wiki". 2008-08-23. http://gpu2.twomurs.com/index.php?title=Main_Page. Retrieved on 2008-11-06.

Folding@home 92

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ps3-folding-kicking-ass-getting-update-255086.php.
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scei.co.jp/folding/en/update.html. Retrieved on 2007-12-31.
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http://blog.us.playstation.eom/2007/12/18/new-foldinghome-features-coming/l "New Folding@home Features

Coming", http://blog.us.playstation.com/2007/12/18/new-foldinghome-features-coming/. Retrieved on

2007-12-31.
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kotaku.com/5051551/life-with-playstation-out-now.
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Stanford University. http://folding.stanford.edu/FAQ-SMP.html. Retrieved on 2006-11-13.
[91] [http://forum. folding-community.org/viewtopic. php?t=8846 Folding-community: why have teams?
[92] http://www.mprize.org/index.php?ctype=news&pagename=blogdetaildisplay&BID=2008032-20053630&detaildisplay=Y|"Th(

Mprize-". http://www.mprize.org/index. php?ctype=news&pagename=blogdetaildisplay&

BID = 2008032-20053630&detaildisplay=Y.
[93] http://folding-community.org/viewtopic.php?p=178218&highlight=#178218|"Why not OpenSource?". http://

folding-community, org/viewtopic. php?p =17821 8&highlight= #178218.
[94] http://folding. Stanford. edu/English/FAQ-OpenSource|"Folding@home Open Source FAQ". http://folding.

stanford.edu/English/FAQ-OpenSource.
[95] http://folding. Stanford. edu/English/FAQ-highperformance|"FAH on BOINC". Folding@home high performance

client FAQ. http://folding.stanford.edu/English/FAQ-highperformance.
[96] http://www. Stanford. edu/group/pandegroup/folding/FAQ-PS3.html|"PS3 FAQ" (FAQ), http ://www. Stanford.

edu/group/pandegroup/folding/FAQ-PS3.html.
[97] http://green500.org/lists/listdisplay. php?month=ll&year=2008&Iist=green500_200811.csv&start=l&Iine= 101 |"Green

500". http://green500.org/lists/listdisplay.php ?month=ll&year=2008&list=green500_200811.csv&

start=l&line=101.
[98] http://green500.org/lists/2008/ll/list.phprThe Green500 List", http://green500.org/lists/2008/ll/list.

php. Retrieved on 2008-12-27.
[99] http://en.wikipedia.0rg/wiki/Windmill#M0dern Windmills I "Windmill - Wikipedia, the free encyclopedia", http:/

/en. wikipedia. org/wiki/Windmill#Modern_Windmills.

External links

• Folding@home project homepage (http://folding.stanford.edu/)

• Folding@home Results (published papers) (http://folding.stanford.edu/Papers/)

• FAH blog (http://folding.typepad.com/)

• FAH Forum (http://foldingforum.org/)

• Folding@home Wiki (http://fahwiki.net/index.php/Main_Page)

• Official Folding@home Stats (http://folding.stanford.edu/English/Stats)

• Extreme OC Folding@home Stats (http://folding.ExtremeOverClocking.com/)

• Kakao Folding@home Stats (http://kakaostats.com/)

• Wikipedia team (http://fah-web. Stanford. edu/cgi-bin/main.py?qtype=teampage&
teamnum=42223)

• Massive folding farm (http://www.overclock.net/overclock-net-folding-home-team/
370859-nitteo-s-f-h-gpu2-farm.html) Pics of a dedicated contributor's installation

• FoldWatcher (http://sourceforge.net/projects/foldwatcher) A Folding@Home
monitoring application

Folding@home 93

Multi-media links

• Talk given by Folding@home author Vijay Pande at the PARC forum (http://www.parc.
com/cms/get_article.php?id=799)

• Folding@home Instructional Video on YouTube (http://www.youtube.com/
watch?v=2BVNCQt6MJw)

• Interview of Vijay Pande about Folding@Home Project (http://www.ustream.tv/
recorded/1070617)

Folding@home 94

Molecular Dynamics, Theories and
Computational Methods

Classical mechanics

In physics, classical mechanics is one of the two major sub-fields of study in the science
of mechanics, which is concerned with the set of physical laws governing and
mathematically describing the motions of bodies and aggregates of bodies geometrically
distributed within a certain boundary under the action of a system of forces. The other
sub-field is quantum mechanics.

Classical mechanics is used for describing the motion of macroscopic objects, from
projectiles to parts of machinery, as well as astronomical objects, such as spacecraft,
planets, stars, and galaxies. It produces very accurate results within these domains, and is
one of the oldest and largest subjects in science, engineering and technology.

Besides this, many related specialties exist, dealing with gases, liquids, and solids, and so
on. Classical mechanics is enhanced by special relativity for objects moving with high
velocity, approaching the speed of light; general relativity is employed to handle gravitation
at a deeper level; and quantum mechanics handles the wave-particle duality of atoms and
molecules.

The term classical mechanics was coined in the early 20th century to describe the system of
mathematical physics begun by Isaac Newton and many contemporary 17th century natural
philosophers, building upon the earlier astronomical theories of Johannes Kepler, which in
turn were based on the precise observations of Tycho Brahe and the studies of terrestrial
projectile motion of Galileo, but before the development of quantum physics and relativity.
Therefore, some sources exclude so-called "relativistic physics" from that category.
However, a number of modern sources do include Einstein's mechanics, which in their view
represents classical mechanics in its most developed and most accurate form. The initial
stage in the development of classical mechanics is often referred to as Newtonian
mechanics, and is associated with the physical concepts employed by and the mathematical
methods invented by Newton himself, in parallel with Leibniz, and others. This is further
described in the following sections. More abstract and general methods include Lagrangian
mechanics and Hamiltonian mechanics. Much of the content of classical mechanics was
created in the 18th and 19th centuries and extends considerably beyond (particularly in its
use of analytical mathematics) the work of Newton.

Classical mechanics

max

Description of the theory

The following introduces the basic concepts of classical
mechanics. For simplicity, it often models real-world
objects as point particles, objects with negligible size.
The motion of a point particle is characterized by a
small number of parameters: its position, mass, and the
forces applied to it. Each of these parameters is
discussed in turn.

In reality, the kind of objects which classical mechanics

can describe always have a non-zero size. (The physics

of very small particles, such as the electron, is more

accurately described by quantum mechanics). Objects

with non-zero size have more complicated behavior

than hypothetical point particles, because of the

additional degrees of freedom— for example, a baseball

can spin while it is moving. However, the results for point particles can be used to study

such objects by treating them as composite objects, made up of a large number of

interacting point particles. The center of mass of a composite object behaves like a point

particle.

The analysis of projectile motion is a
part of classical mechanics.

Position and its derivatives

The SI derived "mechanical"

(that is, not electromagnetic or thermal)

units with kg, m and s

Position

Angular position/ Angle

unitless (radian)

velocity

m s _1

Angular velocity

s" 1

acceleration

m s~

Angular acceleration

s" 2

jerk

m s" 3

"Angular jerk"

s" 3

specific energy

m 2 s" 2

absorbed dose rate

m 2 s" 3

moment of inertia

kg m 2

momentum

kg m s~

angular momentum

kg m 2 s~

force

kg m s~

torgue

kg m 2 s~

Classical mechanics

energy

kg m 2 s~ 2

power

kg m 2 s~

pressure and energy density

kg m~ s~

surface tension

kgs" 2

Spring constant

kgs" 2

irradiance and energy flux

kgs" 3

kinematic viscosity

■> -l
m 2 s

dynamic viscosity

kg m~ s

Density(mass density)

kg m" 3

Densityfweight density)

kg m" 2 s" 2

Number density

m" 3

Action

kg m 2 s~

The position of a point particle is defined with respect to an arbitrary fixed reference point,
O, in space, usually accompanied by a coordinate system, with the reference point located
at the origin of the coordinate system. It is defined as the vector r from O to the particle. In
general, the point particle need not be stationary relative to O, so r is a function of t, the
time elapsed since an arbitrary initial time. In pre-Einstein relativity (known as Galilean
relativity), time is considered an absolute, i.e., the time interval between any given pair of
events is the same for all observers. In addition to relying on absolute time, classical

mechanics assumes Euclidean geometry for the structure of space.

[l]

Velocity and speed

The velocity, or the rate of change of position with time, is defined as the derivative of the
position with respect to time or

&= —

at '

In classical mechanics, velocities are directly additive and subtractive. For example, if one
car traveling East at 60 km/h passes another car traveling East at 50 km/h, then from the
perspective of the slower car, the faster car is traveling east at 60 - 50 = 10 km/h.
Whereas, from the perspective of the faster car, the slower car is moving 1 km/h to the
West. Velocities are directly additive as vector quantities; they must be dealt with using
vector analysis.

Mathematically, if the velocity of the first object in the previous discussion is denoted by
the vector u = ud and the velocity of the second object by the vector v = ve where «is
the speed of the first object, wis the speed of the second object, and ^ and e*are unit
vectors in the directions of motion of each particle respectively, then the velocity of the first
object as seen by the second object is:

u' = U — V
Similarly:

v = v

Classical mechanics 97

When both objects are moving in the same direction, this equation can be simplified to:

u' = (u — v)d
Or, by ignoring direction, the difference can be given in terms of speed only:

u = u — v

Acceleration

The acceleration, or rate of change of velocity, is the derivative of the velocity with respect
to time (the second derivative of the position with respect to time) or

dt
Acceleration can arise from a change with time of the magnitude of the velocity or of the

direction of the velocity or both. If only the magnitude, v , of the velocity decreases, this is

sometimes referred to as deceleration, but generally any change in the velocity with time,

including deceleration, is simply referred to as acceleration.

Frames of reference

While the position and velocity and acceleration of a particle can be referred to any
observer in any state of motion, classical mechanics assumes the existence of a special
family of reference frames in terms of which the mechanical laws of nature take a
comparatively simple form. These special reference frames are called inertial frames. They
are characterized by the absence of acceleration of the observer and the requirement that
all forces entering the observer's physical laws originate in identifiable sources (charges,
gravitational bodies, and so forth). A non-inertial reference frame is one accelerating with
respect to an inertial one, and in such a non-inertial frame a particle is subject to
acceleration by fictitious forces that enter the equations of motion solely as a result of its
accelerated motion, and do not originate in identifiable sources. These fictitious forces are
in addition to the real forces recognized in an inertial frame. A key concept of inertial
frames is the method for identifying them. (See inertial frame of reference for a discussion.)
For practical purposes, reference frames that are unaccelerated with respect to the distant
stars are regarded as good approximations to inertial frames.

The following consequences can be derived about the perspective of an event in two inertial
reference frames, 5'and S' , where S'is traveling at a relative velocity of cto S .

• !?=£-£ (the velocity Joi a particle from the perspective of S' is slower by £than its
velocity rfrom the perspective of S)

• 5=3. (the acceleration of a particle is the same in any inertial reference frame)

• F>=F (the force on a particle is the same in any inertial reference frame)

• the speed of light is not a constant in classical mechanics, nor does the special position
given to the speed of light in relativistic mechanics have a counterpart in classical
mechanics.

• the form of Maxwell's equations is not preserved across such inertial reference frames.
However, in Einstein's theory of special relativity, the assumed constancy (invariance) of
the vacuum speed of light alters the relationships between inertial reference frames so as
to render Maxwell's equations invariant.

Classical mechanics 98

Forces; Newton's Second Law

Newton was the first to mathematically express the relationship between force and
momentum. Some physicists interpret Newton's second law of motion as a definition of
force and mass, while others consider it to be a fundamental postulate, a law of nature.
Either interpretation has the same mathematical consequences, historically known as
"Newton's Second Law":

-+ dp d(mv)

' ~ dt ' dt '
The quantity mvis called the (canonical) momentum. The net force on a particle is thus
equal to rate chanqe of momentum of the particle with time. Since the definition of

dv
leration is a =

form

acceleration is a = — , the second law can be written in the simplified and more familiar

F = ma-
So lonq as the force actinq on a particle is known, Newton's second law is sufficient to
describe the motion of a particle. Once independent relations for each force actinq on a
particle are available, they can be substituted into Newton's second law to obtain an
ordinary differential equation, which is called the equation of motion.

As an example, assume that friction is the only force actinq on the particle, and that it may
be modeled as a function of the velocity of the particle, for example:

F R = -Xv
with A a positive constant. Then the equation of motion is

—Xv = ma = m — .

This can be inteqrated to obtain

v = v e-* t/m
where Wois the initial velocity. This means that the velocity of this particle decays
exponentially to zero as time proqresses. In this case, an equivalent viewpoint is that the
kinetic enerqy of the particle is absorbed by friction (which converts it to heat enerqy in
accordance with the conservation of enerqy), slowinq it down. This expression can be
further inteqrated to obtain the position Fof the particle as a function of time.
Important forces include the qravitational force and the Lorentz force for
electromaqnetism. In addition, Newton's third law can sometimes be used to deduce the
forces actinq on a particle: if it is known that particle A exerts a force J^on another particle
B, it follows that B must exert an equal and opposite reaction force, —F, on A. The stronq
form of Newton's third law requires that J^and —fact alonq the line connectinq A and B,
while the weak form does not. Illustrations of the weak form of Newton's third law are often
found for maqnetic forces.

Classical mechanics 99

Energy

If a force pis applied to a particle that achieves a displacement Af , the work done by the
force is defined as the scalar product of force and displacement vectors: (noting that the
displacement vector is the change in position vector)

W = FAr-

If the mass of the particle is constant, and W" is the total work done on the particle,
obtained by summing the work done by each applied force, from Newton's second law:

W batal = AE k ,
where E is called the kinetic energy. For a point particle, it is mathematically defined as
the amount of work done to accelerate the particle from zero velocity to the given velocity

r 1 2

E k = pnv .
For extended objects composed of many particles, the kinetic energy of the composite body
is the sum of the kinetic energies of the particles.

A particular class of forces, known as conservative forces, can be expressed as the gradient
of a scalar function, known as the potential energy and denoted E :

F = -VE p .
If all the forces acting on a particle are conservative, and E is the total potential energy
(which is defined as a work of involved forces to rearrange mutual positions of bodies),
obtained by summing the potential energies corresponding to each force

F ■ Af = -VE p ■ As = -AE P => -AE p = AE k => A(E k + E p ) = 0.
This result is known as conservation of energy and states that the total energy,

is constant in time. It is often useful, because many commonly encountered forces are
conservative.

Beyond Newton's Laws

Classical mechanics also includes descriptions of the complex motions of extended
non-pointlike objects. Euler's laws provide extensions to Newton's laws in this area. The
concepts of angular momentum rely on the same calculus used to describe one-dimensional
motion.

There are two important alternative formulations of classical mechanics: Lagrangian
mechanics and Hamiltonian mechanics. These, and other modern formulations, usually
bypass the concept of "force", instead referring to other physical quantities, such as energy,
for describing mechanical systems.

Classical transformations

Consider two reference frames S and S' . For observers in each of the reference frames an
event has space-time coordinates of (x,y,z,£) in frame S and (x' ,y' ,z' ,V ) in frame S' .
Assuming time is measured the same in all reference frames, and if we require x = x' when
t = 0, then the relation between the space-time coordinates of the same event observed
from the reference frames S' and S, which are moving at a relative velocity of u in the x

Classical mechanics 100

direction is:
x' = x - ut

y = y

z' = z

V = t
This set of formulas defines a group transformation known as the Galilean transformation
(informally, the Galilean transform) . This group is a limiting case of the Poincare group
used in special relativity. The limiting case applies when the velocity u is very small
compared to c, the speed of light.

For some problems, it is convenient to use rotating coordinates (reference frames). Thereby
one can either keep a mapping to a convenient inertial frame, or introduce additionally a
fictitious centrifugal force and Coriolis force.

History

Some Greek philosophers of antiquity, among them Aristotle, may have been the first to
maintain the idea that "everything happens for a reason" and that theoretical principles can
assist in the understanding of nature. While to a modern reader, many of these preserved
ideas come forth as eminently reasonable, there is a conspicuous lack of both mathematical
theory and controlled experiment, as we know it. These both turned out to be decisive
factors in forming modern science, and they started out with classical mechanics.

An early experimental scientific method was introduced into mechanics in the 11th century
by al-Biruni, who along with al-Khazini in the 12th century, unified statics and dynamics
into the science of mechanics, and combined the fields of hydrostatics with dynamics to
create the field of hydrodynamics. Concepts related to Newton's laws of motion were also
enunciated by several other Muslim physicists during the Middle Ages. Early versions of the
law of inertia, known as Newton's first law of motion, and the concept relating to
momentum, part of Newton's second law of motion, were described by Ibn al-Haytham
(Alhacen) and Avicenna. The proportionality between force and acceleration, an

important principle in classical mechanics, was first stated by Hibat Allah Abu'l-Barakat

T71

al-Baghdaadi, and theories on gravity were developed by Ja'far Muhammad ibn Musa ibn
Shakir, [8] Ibn al-Haytham, [9] and al-Khazini. [10] It is known that Galileo Galilei's
mathematical treatment of acceleration and his concept of impetus grew out of earlier
medieval analyses of motion, especially those of Avicenna, Ibn Bajjah, and Jean
Buridan.

The first published causal explanation of the motions of planets was Johannes Kepler's
Astronomia nova published in 1609. He concluded, based on Tycho Brahe's observations of
the orbit of Mars, that the orbits were ellipses. This break with ancient thought was
happening around the same time that Galilei was proposing abstract mathematical laws for
the motion of objects. He may (or may not) have performed the famous experiment of
dropping two cannon balls of different masses from the tower of Pisa, showing that they
both hit the ground at the same time. The reality of this experiment is disputed, but, more
importantly, he did carry out quantitative experiments by rolling balls on an inclined plane.
His theory of accelerated motion derived from the results of such experiments, and forms a
cornerstone of classical mechanics.

Classical mechanics 101

As foundation for his principles of natural philosophy, Newton proposed three laws of
motion: the law of inertia, his second law of acceleration (mentioned above), and the law of
action and reaction; and hence laid the foundations for classical mechanics. Both Newton's
second and third laws were given proper scientific and mathematical treatment in Newton's
Philosophiae Naturalis Principia Mathematica, which distinguishes them from earlier
attempts at explaining similar phenomena, which were either incomplete, incorrect, or
given little accurate mathematical expression. Newton also enunciated the principles of
conservation of momentum and angular momentum. In Mechanics, Newton was also the
first to provide the first correct scientific and mathematical formulation of gravity in
Newton's law of universal gravitation. The combination of Newton's laws of motion and
gravitation provide the fullest and most accurate description of classical mechanics. He
demonstrated that these laws apply to everyday objects as well as to celestial objects. In
particular, he obtained a theoretical explanation of Kepler's laws of motion of the planets.

Newton previously invented the calculus, of mathematics, and used it to perform the
mathematical calculations. For acceptability, his book, the Principia, was formulated
entirely in terms of the long established geometric methods, which were soon to be eclipsed
by his calculus. However it was Leibniz who developed the notation of the derivative and
integral preferred today.

Newton, and most of his contemporaries, with the notable exception of Huygens, worked on
the assumption that classical mechanics would be able to explain all phenomena, including
light, in the form of geometric optics. Even when discovering the so-called Newton's rings
(a wave interference phenomenon) his explanation remained with his own corpuscular
theory of light.

After Newton, classical mechanics became a principal field of study in mathematics as well
as physics.

Some difficulties were discovered in the late 19th century that could only be resolved by
more modern physics. Some of these difficulties related to compatibility with
electromagnetic theory, and the famous Michelson-Morley experiment. The resolution of
these problems led to the special theory of relativity, often included in the term classical
mechanics.

A second set of difficulties were related to thermodynamics. When combined with
thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical
mechanics, in which entropy is not a well-defined quantity. Black-body radiation was not
explained without the introduction of quanta. As experiments reached the atomic level,
classical mechanics failed to explain, even approximately, such basic things as the energy
levels and sizes of atoms and the photo-electric effect. The effort at resolving these
problems led to the development of quantum mechanics.

Since the end of the 20th century, the place of classical mechanics in physics has been no
longer that of an independent theory. Emphasis has shifted to understanding the
fundamental forces of nature as in the Standard model and its more modern extensions into

MO]

a unified theory of everything. 1 J Classical mechanics is a theory for the study of the
motion of non-quantum mechanical, low-energy particles in weak gravitational fields.

Classical mechanics

102

Far less than 3x10 8 m/s

Comparable to 3x10 8 m/s

Limits of validity

Many branches of classical
mechanics are simplifications
or approximations of more
accurate forms; two of the
most accurate being general
relativity and relativistic
statistical mechanics.

Geometric optics is an
approximation to the quantum
theory of light, and does not
have a superior "classical"
form.

The Newtonian
approximation to
special relativity

Newtonian, or non-relativistic
classical momentum

p = m u
is the result of the first order Taylor approximation of the relativistic expression:

Classical
Mechanics

Relativistic
Mechanics

Quantum
Mechanics

Quantum
Field Theory

Domain of validity for Classical Mechanics

P =

m v

1 2
1 V

= m v\ 1 + --j +

where v = \v\

when expanded about

- =

so it is only valid when the velocity is much less than the speed of light. Quantitatively
speaking, the approximation is good so long as

<<1

For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage

magnetron is given by J ~ Jc Tle % ' wnere J c ^ s the classical frequency of an electron

(or other charged particle) with kinetic energy Tand (rest) mass m o circling in a magnetic
field. The (rest) mass of an electron is 511 keV. So the frequency correction is 1% for a
magnetic vacuum tube with a 5.11 kV. direct current accelerating voltage.

Classical mechanics

103

The classical approximation to quantum mechanics

The ray approximation of classical mechanics breaks down when the de Broglie wavelength
is not much smaller than other dimensions of the system. For non-relativistic particles, this
wavelength is

x= h -

P
where h is Planck's constant and p is the momentum.

Again, this happens with electrons before it happens with heavier particles. For example,
the electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 volts,
had a wave length of 0.167 nm, which was long enough to exhibit a single diffraction side
lobe when reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With
a larger vacuum chamber, it would seem relatively easy to increase the angular resolution
from around a radian to a milliradian and see quantum diffraction from the periodic
patterns of integrated circuit computer memory.

More practical examples of the failure of classical mechanics on an engineering scale are
conduction by quantum tunneling in tunnel diodes and very narrow transistor gates in
integrated circuits.

Classical mechanics is the same extreme high frequency approximation as geometric optics.
It is more often accurate because it describes particles and bodies with rest mass. These
have more momentum and therefore shorter De Broglie wavelengths than massless
particles, such as light, with the same kinetic energies.

Branches

Classical mechanics was traditionally divided into three
main branches:

• Statics, the study of equilibrium and its relation to
forces

• Dynamics, the study of motion and its relation to
forces

• Kinematics, dealing with the implications of observed
motions without regard for circumstances causing
them

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Branches of mechanics

Another division is based on the choice of mathematical
formalism:

• Newtonian mechanics

• Lagrangian mechanics

• Hamiltonian mechanics

Alternatively, a division can be made by region of application:

• Celestial mechanics, relating to stars, planets and other celestial bodies

• Continuum mechanics, for materials which are modelled as a continuum, e.g., solids and
fluids (i.e., liquids and gases).

• Relativistic mechanics (i.e. including the special and general theories of relativity), for
bodies whose speed is close to the speed of light.

Classical mechanics 104

• Statistical mechanics, which provides a framework for relating the microscopic
properties of individual atoms and molecules to the macroscopic or bulk thermodynamic
properties of materials.

See also

• History of classical mechanics

• Dynamical systems

• List of equations in classical mechanics

• List of publications in classical mechanics

• Molecular dynamics

• Newton's laws of motion

• Special theory of relativity

Notes

[I] MIT physics 8.01 lecture notes (page 12) (http://ocw.mit.edu/NR/rdonlyres/Physics/8-01Physics-IFall2003/
B4144452-A6DE-464D-A0FA-D4D057AA9222/0/binderl.pdf) (PDF)

[2] Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", in Roshdi Rashed, ed., Encyclopedia of the History of

Arabic Science, Vol. 2, p. 614-642 [642], Routledge, London and New York
[3] Abdus Salam (1984), "Islam and Science". In C. H. Lai (1987), Ideals and Realities: Selected Essays ofAbdus

Salam, 2nd ed., World Scientific, Singapore, p. 179-213.
[4] Seyyed Hossein Nasr, "The achievements of Ibn Sina in the field of science and his contributions to its

philosophy", Islam & Science, December 2003.
[5] Fernando Espinoza (2005). "An analysis of the historical development of ideas about motion and its

implications for teaching", Physics Education 40 (2), p. 141.
[6] Seyyed Hossein Nasr, "Islamic Conception Of Intellectual Life", in Philip P. Wiener (ed.), Dictionary of the

History of Ideas, Vol. 2, p. 65, Charles Scribner's Sons, New York, 1973-1974.
[7] Shlomo Pines (1970). "Abu'l-Barakat al-Baghdadi, Hibat Allah". Dictionary of Scientific Biography. 1. New

York: Charles Scribner's Sons. pp. 26-28. ISBN 0684101149.

(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", Journal of the History

of Ideas 64 (4), p. 521-546 [528]
[8] Robert Briffault (1938). The Making of Humanity, p. 191.
[9] Nader El-Bizri (2006), "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006), Medieval Islamic Civilization: An

Encyclopaedia, Vol. II, p. 343-345, Routledge, New York, London.
[10] Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", in Roshdi Rashed, ed., Encyclopaedia of the History

of Arabic Science, Vol. 2, p. 622. London and New York: Routledge.

[II] Galileo Galilei, Two New Sciences, trans. Stillman Drake, (Madison: Univ. of Wisconsin Pr., 1974), pp 217,
225, 296-7.

[12] Ernest A. Moody (1951). "Galileo and Avempace: The Dynamics of the Leaning Tower Experiment (I)", Journal

of the History of Ideas 12 (2), p. 163-193.
[13] Page 2-10 of the Feynman Lectures on Physics says "For already in classical mechanics there was

indeterminability from a practical point of view." The past tense here implies that classical physics is no longer

fundamental.

Classical mechanics 105

References

Feynman, Richard (1996). Six Easy Pieces. Perseus Publishing. ISBN 0-201-40825-2.

Feynman, Richard; Phillips, Richard (1998). Six Easy Pieces. Perseus Publishing. ISBN

0-201-32841-0.

Feynman, Richard (1999). Lectures on Physics. Perseus Publishing. ISBN 0-7382-0092-1.

Landau, L. D.; Lifshitz, E. M. (1972). Mechanics Course of Theoretical Physics , Vol. 1.

Franklin Book Company. ISBN 0-08-0 16739-X.

Kleppner, D. and Kolenkow, R. J., An Introduction to Mechanics, McGraw-Hill (1973).

ISBN 0-07-035048-5

Gerald Jay Sussman and Jack Wisdom, Structure and Interpretation of Classical

Mechanics, MIT Press (2001). ISBN 0-262-19455-4}

Herbert Goldstein, Charles P. Poole, John L. Safko, Classical Mechanics (3rd Edition),

Addison Wesley; ISBN 0-201-65702-3

Robert Martin Eisberg, Fundamentals of Modern Physics, John Wiley and Sons, 1961

M. Alonso, J. Finn, "Fundamental university physics", Addison-Wesley

External links

Crowell, Benjamin. Newtonian Physics (http://www.lightandmatter.com/arealbookl.

html) (an introductory text, uses algebra with optional sections involving calculus)

Fitzpatrick, Richard. Classical Mechanics (http://farside.ph.utexas.edu/teaching/301/

301.html) (uses calculus)

Hoiland, Paul (2004). Preferred Frames of Reference & Relativity (http://doc.cern. ch//

archive/electronic/other/ ext/ext-2 004-1 26.pdf)

Horbatsch, Marko, " Classical Mechanics Course Notes (http://www.yorku.ca/marko/

PHYS2010/index.htm)".

Rosu, Haret C, " Classical Mechanics (http://arxiv.org/abs/physics/9909035)". Physics

Education. 1999. [arxiv.org : physics/9909035]

Schiller, Christoph. Motion Mountain (http://www.motionmountain.net) (an

introductory text, uses some calculus; see also Motion Mountain)

Sussman, Gerald Jay & Wisdom, Jack & Mayer,Meinhard E. (2001). Structure and

Interpretation of Classical Mechanics (http://mitpress.mit.edu/SICM/)

Tong, David. Classical Dynamics (http://www.damtp.cam.ac.uk/user/tong/dynamics.

html) (Cambridge lecture notes on Lagrangian and Hamiltonian formalism)

Kinematic Models for Design Digital Library (KMODDL) (http://kmoddl. library. Cornell.

edu/index.php)

Movies and photos of hundreds of working mechanical-systems models at Cornell

University. Also includes an e-book library (http://kmoddl.library.cornell.edu/e-books.

php) of classic texts on mechanical design and engineering.

Newton's laws of motion

106

Newton's laws of motion

Newton's laws of motion are three physical laws
that form the basis for classical mechanics. They
are:

1 . A body at rest stays at rest, and a body in motion
stays in motion, unless it is acted on by an external
force.

2. Force equals mass times acceleration (F = ma)
(or alternately, force equals the time rate of chanqe
of momentum).

3. To every action there is an equal and opposite
reaction.

They describe the relationship between the forces
actinq on a body to the motion of the body. They
were first compiled by Sir Isaac Newton in his work
Philosophies Naturalis Principia Mathematica, first
published on July 5, 1687. Newton used them to
explain and investiqate the motion of many physical
objects and systems. For example, in the third
volume of the text, Newton showed that these laws
of motion, combined with his law of universal
qravitation, explained Kepler's laws of planetary
motion.

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Newton's First and Second laws, in Latin,

from the original 1687 edition of the

Principia Mathematica.

The three laws

First law

There exists a set of inertial reference frames relative to which all particles with no net
force actinq on them will move without chanqe in their velocity. This law is often
simplified as "A body persists its state of rest or of uniform motion unless acted upon
by an external unbalanced force." Newton's first law is often referred to as the law of
inertia.

Second law

Observed from an inertial reference frame, the net force on a particle is proportional
to the time rate of chanqe of its linear momentum: F = d(mv)/dt. This law is often
stated as, "Force equals mass times acceleration (F = ma)": the net force on an object
is equal to the mass of the object multiplied by its acceleration.

Third law

Whenever a particle A exerts a force on another particle B, B simultaneously exerts a
force on A with the same maqnitude in the opposite direction. The stronq form of the
law further postulates that these two forces act alonq the same line. This law is often
simplified into the sentence, "To every action there is an equal and opposite reaction."

Newton's laws of motion 107

In the given interpretation mass, acceleration, momentum, and (most importantly) force are
assumed to be externally defined quantities. This is the most common, but not the only
interpretation: one can consider the laws to be a definition of these quantities. Notice that
the second law only holds when the observation is made from an inertial reference frame,
and since an inertial reference frame is defined by the first law, asking a proof of the first
law from the second law is a logical fallacy. At speeds approaching the speed of light the
effects of special relativity must be taken into account.

Newton's first law: law of inertia

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter
in directum, nisi quatenus a viribus impressis cogitur statum ilium mutare. Every
body persists in its state of being at rest or of moving uniformly straight
forward, except insofar as it is compelled to change its state by force
impressed.

Newton's first law is also called the law of inertia. In a simplified form, it states that if the
vector sum of all forces (also known as the net force) acting on an object is zero, then the
state of motion of the object does not change. In particular: Newton's first law: An object at
rest remains at rest and an object in motion will remain in motion unless acted on by an
unbalanced force.

• An object that is not moving will not move until a net force acts upon it.

• An object that is moving will not change its velocity (accelerate) until a net force acts
upon it.

The first point needs no comment, but the second seems to violate everyday experience. A
hockey puck sliding along a table doesn't move forever; rather, it slows and eventually
comes to a stop. According to Newton's laws, though, the hockey puck does not stop of its
own accord, but because of a force applied in the opposite direction to the direction of
motion. That force is easily identified as a frictional force between the table and the puck.
In the absence of such a force, as approximated by an air hockey table or ice rink, the
puck's motion would not slow.

There are no perfect demonstrations of the law, as friction usually causes a force to act on a
moving body, and even in outer space gravitational forces act and cannot be shielded
against, but the law serves to emphasize the elementary causes of changes in an object's
state of motion.

The above treatment of Newton's first law is an over-simplification, though. A more
sophisticated approach to the law of inertia is given by:

There is a class of frames of reference (called inertial frames) relative to
which the motion of a particle not subject to forces is a straight line.

Newton placed the law of inertia first to establish frames of reference for which the other
laws are applicable (see Gailili & Tseitlin, or Woodhouse ). Such frames are called
inertial frames.

To understand why the laws are restricted to inertial frames, consider a ball at rest within
an accelerating body: an airplane on a runway will suffice for this example. From the
perspective of anyone within the airplane (that is, from the airplane's frame of reference
when put in technical terms) the ball will appear to move backwards as the plane
accelerates forwards (the same feeling as being pushed back into your seat as the plane

Newton's laws of motion 108

accelerates). This motion appears to contradict Newton's second law as, from the point of
view of the passengers, there appears to be no force acting on the ball that would cause it
to move. The reason why there is in fact no contradiction to the second law is because
Newton's second law (without modification) is not applicable in this situation: Newton's
first law does not apply because the stationary ball does not remain stationary. Thus, it is
important to establish whether the various laws are applicable or not, inasmuch as they are
not applicable in all situations. ^

History of the Law of Inertia

Newton's first law is a restatement of what Galileo had already described and Newton gave
credit to Galileo. It differs from Aristotle's view that all objects have a natural place in the
universe. Aristotle believed that heavy objects like rocks wanted to be at rest on the Earth
and that light objects like smoke wanted to be at rest in the sky and the stars wanted to
remain in the heavens. However, a key difference between Galileo's idea and Aristotle's is
that Galileo realized that force acting on a body determines acceleration, not velocity. This
insight leads to Newton's First Law— no force means no acceleration, and hence the body
will maintain its velocity.

The law of inertia apparently occurred to several different natural philosophers and
scientists independently. The inertia of motion was described in the 3rd century BC by the
Chinese philosopher Mo Tzu, and in the 11th century by the Muslim scientists, Alhazem ]
and Avicenna. The 17th century philosopher Rene Descartes also formulated the law,
although he did not perform any experiments to confirm it.

Newton's second law

Lex II: Mutationem motus proportionalem esse vz motrici impressae, et fieri secundum
lineam rectam qua vis ilia imprimitur.

The change of momentum of a body is proportional to the impulse impressed
on the body, and happens along the straight line on which that impulse is
impressed.

In Motte's 1729 translation (from Newton's Latin), the second law of motion reads:

LAW II: The alteration of motion is ever proportional to the motive force
impressed; and is made in the direction of the right line in which that force is
impressed. — If a force generates a motion, a double force will generate double
the motion, a triple force triple the motion, whether that force be impressed
altogether and at once, or gradually and successively. And this motion (being
always directed the same way with the generating force), if the body moved
before, is added to or subtracted from the former motion, according as they
directly conspire with or are directly contrary to each other; or obliquely joined,
when they are oblique, so as to produce a new motion compounded from the
determination of both.

Using modern symbolic notation, Newton's second law can be written as a vector
differential equation:

d(mv) dv

where F is the force vector, m is the mass of the body, v is the velocity vector and t is time.

Newton's laws of motion 109

The product of the mass and velocity is momentum (which Newton himself called "quantity
of motion"). Therefore, this equation expresses the physical relationship between force and
momentum for a body with constant mass. Because the law describes the motion of bodies
of constant mass only , the mass can be moved outside the differential operator.

The equation implies that, under zero net force, the momentum of a body is also constant.
However, any mass that is qained or lost by the body will cause a chanqe in momentum that
is not the result of an external force. This equation does not hold in such cases. See open
systems.

It should be noted that, as is consistent with the law of inertia, the time derivative of the
momentum is non-zero when the momentum chanqes direction, even if there is no chanqe
in its magnitude. See time derivative.

By substitution usinq the definition of acceleration, this differential equation can be
rewritten in a more familiar form

F = 772a
where

a = — — .
dt

A verbal equivalent of this is "the acceleration of an object is proportional to the force
applied, and inversely proportional to the mass of the object". In qeneral, at slow speeds
(slow relative to the speed of liqht), the relationship between momentum and velocity is
approximately linear. Nearly all speeds within the human experience fall within this
cateqory. At hiqher speeds, however, this approximation becomes increasinqly inaccurate
and the theory of special relativity must be applied.

Impulse

The term impulse is closely related to the second law, and historically speakinq is closer to
the oriqinal meaninq of the law. The meaninq of an impulse is as follows:

An impulse occurs when a force F acts over an interval of time At and is qiven by

/ Fdt.

The words motive force were used by Newton to describe "impulse" and motion to describe
momentum; consequently, a historically closer readinq of the second law describes the
relation between impulse and chanqe of momentum. That is, a mathematical renderinq of
the oriqinal wordinq resembles a finite difference version of the second law, such as

I = Ap = mAv

where I is the impulse, Ap is the chanqe in momentum, m is the mass, and Av is the chanqe
in velocity.

rioi

The analysis of collisions and impacts uses the impulse concept.

Newton's laws of motion 110

Relativity

Main article: Special Relativity

Open systems

So-called variable mass systems that are not closed systems, like a rocket burning fuel and

ejecting spent gases, can not be directly treated by making mass a function of time in the

ri2i ri3i
second law. The reasoning, given in An Introduction to Mechanics by Kleppner and

Kolenkow and other modern texts, is that Newton's second law applies fundamentally to

particles. In classical mechanics, particles by definition have constant mass. In case of

well-defined systems of particles, Newton's law can be extended by summing over all the

particles in the system. In this case, we have to refer all vectors to the center of mass.

Applying the second law to extended objects implicitly assumes the object to be a

well-defined collection of particles. However, 'variable mass' systems like a rocket or a

leaking bucket do not consist of a set number of particles. They are not well-defined

systems. Therefore Newton's second law can not be applied to them directly.

The general equation of motion for a body whose mass m varies with time by either ejecting
or accreting mass is obtained by rearranging the second law and adding a term to account
for the momentum carried by mass entering or leaving the system,

F nc t + U-r^ = m~

dm dv

— — =m—
dt dt

where u is the relative velocity of the escaping or incoming mass with respect to the center
of mass of the body. Under some conventions, the quantity u*dm/d£ on the left-hand side is
defined as a force (the force exerted on the body by the changing mass, such as rocket
exhaust) and is included in the quantity F . Then, by substituting the definition of
acceleration, the equation becomes, once again,

F not = ma.

Newton's laws of motion

111

Newton's third law. The skaters' forces on each other
are equal in magnitude, but act in opposite directions.

Newton's third law: law of reciprocal actions

Lex III: Actioni contrariam semper et aequalem esse reactionem: sive corporum
duorum actiones in se mutuo semper esse asquales et in partes contrarias dirigi.

For a force there is always an equal and opposite reaction: or the forces of two
bodies on each other are always equal and are directed in opposite directions.

A more direct translation is:

LAW III: To every action there is

always opposed an equal

reaction: or the mutual actions of

two bodies upon each other are

always equal, and directed to

contrary parts. — Whatever

draws or presses another is as

much drawn or pressed by that

other. If you press a stone with

your finqer, the finqer is also

pressed by the stone. If a horse

draws a stone tied to a rope, the

horse (if I may so say) will be

equally drawn back towards the

stone: for the distended rope, by

the same endeavour to relax or unbend itself, will draw the horse as much

towards the stone, as it does the stone towards the horse, and will obstruct the

proqress of the one as much as it advances that of the other. If a body impinqes

upon another, and by its force chanqes the motion of the other, that body also

(because of the equality of the mutual pressure) will underqo an equal chanqe, in

its own motion, toward the contrary part. The chanqes made by these actions are

equal, not in the velocities but in the motions of the bodies; that is to say, if the

bodies are not hindered by any other impediments. For, as the motions are

equally chanqed, the chanqes of the velocities made toward contrary parts are

reciprocally proportional to the bodies. This law takes place also in attractions, as

will be proved in the next scholium.

In the above, as usual, motion is Newton's name for momentum, hence his careful
distinction between motion and velocity.

The Third Law means that all forces are interactions, and thus that there is no such thinq as
a unidirectional force. If body A exerts a force on body B, simultaneously, body B exerts a
force of the same maqnitude body A, both forces actinq alonq the same line. As shown in
the diaqram opposite, the skaters' forces on each other are equal in maqnitude, but act in
opposite directions. Althouqh the forces are equal, the accelerations are not: the less
massive skater will have a qreater acceleration due to Newton's second law. It is important
to note that the action and reaction act on different objects and do not cancel each other
out. The two forces in Newton's third law are of the same type (e.g., if the road exerts a
forward frictional force on an acceleratinq car's tires, then it is also a frictional force that
Newton's third law predicts for the tires pushinq backward on the road).

Newton's laws of motion 112

Newton used the third law to derive the law of conservation of momentum; [ ] however
from a deeper perspective, conservation of momentum is the more fundamental idea
(derived via Noether's theorem from Galilean invariance), and holds in cases where
Newton's third law appears to fail, for instance when force fields as well as particles carry
momentum, and in quantum mechanics.

Importance and range of validity

Newton's laws were verified by experiment and observation for over 200 years, and they
are excellent approximations at the scales and speeds of everyday life. Newton's laws of
motion, together with his law of universal gravitation and the mathematical techniques of
calculus, provided for the first time a unified quantitative explanation for a wide range of
physical phenomena.

These three laws hold to a good approximation for macroscopic objects under everyday
conditions. However, Newton's laws (combined with Universal Gravitation and Classical
Electrodynamics) are inappropriate for use in certain circumstances, most notably at very
small scales, very high speeds (in special relativity, the Lorentz factor must be included in
the expression for momentum along with rest mass and velocity) or very strong
gravitational fields. Therefore, the laws cannot be used to explain phenomena such as
conduction of electricity in a semiconductor, optical properties of substances, errors in
non-relativistically corrected GPS systems and superconductivity. Explanation of these
phenomena requires more sophisticated physical theory, including General Relativity and
Relativistic Quantum Mechanics.

In quantum mechanics concepts such as force, momentum, and position are defined by
linear operators that operate on the quantum state; at speeds that are much lower than the
speed of light, Newton's laws are just as exact for these operators as they are for classical
objects. At speeds comparable to the speed of light, the second law holds in the original
form F = dp/dt, which says that the force is the derivative of the momentum of the object
with respect to time, but some of the newer versions of the second law (such as the
constant mass approximation above) do not hold at relativistic velocities.

Relationship to the conservation laws

In modern physics, the laws of conservation of momentum, energy, and angular momentum
are of more general validity than Newton's laws, since they apply to both light and matter,
and to both classical and non-classical physics.

This can be stated simply, "Momentum, energy and angular momentum cannot be created
or destroyed."

Because force is the time derivative of momentum, the concept of force is redundant and
subordinate to the conservation of momentum, and is not used in fundamental theories (e.g.
quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard
model explains in detail how the three fundamental forces known as gauge forces originate
out of exchange by virtual particles. Other forces such as gravity and fermionic degeneracy
pressure also arise from the momentum conservation. Indeed, the conservation of
4-momentum in inertial motion via curved space-time results in what we call gravitational
force in general relativity theory. Application of space derivative (which is a momentum
operator in quantum mechanics) to overlaping wave functions of pair of fermions (particles

Newton's laws of motion 113

with semi-integer spin) results in shifts of maxima of compound wavefunction away from
each other, which is observable as "repulsion" of fermions.

Newton stated the third law within a world-view that assumed instantaneous action at a
distance between material particles. However, he was prepared for philosophical criticism
of this action at a distance, and it was in this context that he stated the famous phrase "I
feign no hypotheses". In modern physics, action at a distance has been completely
eliminated, except for subtle effects involving quantum entanglement. However in modern
engineering in all practical applications involving the motion of vehicles and satellites, the
concept of action at a distance is used extensively.

Conservation of energy was discovered nearly two centuries after Newton's lifetime, the
long delay occurring because of the difficulty in understanding the role of microscopic and
invisible forms of energy such as heat and infra-red light.

See also

• Scientific laws named after people

• Mercury, orbit of

• Galilean invariance

• Modified Newtonian dynamics

• Lagrangian mechanics

• Hamiltonian mechanics

• Principle of least action

• Euler's laws

References and notes

[1] See the Principia on line at Andrew Motte Translation (http://ia310114.us.archive.Org/2/items/

newtonspmathemaOOnewtrich/newtonspmathemaOOnewtrich.pdf)
[2] Andrew Motte translation of Newton's Principia (1687) Axioms or Laws of Motion (http://members. tripod.

com/~gravitee/ axioms, htm)
[3] In the second law, m must be treated as the relatistic mass, producing the relativistic expression for

momentum, and the third law must be modified to allow for the finite signal propagation speed between distant

interacting particles.
[4] Isaac Newton, The Principia, A new translation by LB. Cohen and A. Whitman, University of California press,

Berkeley 1999.
[5] NMJ Woodhouse (2003).

http://books.google.com/books?id=ggPXQAeeRLgC&printsec=frontcover&dq=isbn=1852334266#PPA6,Ml\Special

relativity. London/Berlin: Springer, p. 6. ISBN 1-85233-426-6. http://books.google.com/

books?id=ggPXQAeeRLgC&printsec=frontcover&dq=isbn=1852334266#PPA6,Ml.
[6] Galili, I. & Tseitlin, M. (2003), "Newton's first law: text, translations, interpretations, and physics education.",

Science and Education 12 (1): 45-73, doi: 10.1023/A:1022632600805 (http://dx.doi.org/10.1023/

A:1022632600805)
[7] On a more technical note, although Newton's laws are not applicable on non-inertial frames of reference, such

as the accelerating airplane, they can be made to do so with the introduction of a "fictitious force" acting on the

entire system: basically, by introducing a force that quantifies the anomalous motion of objects within that

system (such as the ball moving without an apparent influence in the example above
[8] Abdus Salam (1984), "Islam and Science". In C. H. Lai (1987), Ideals and Realities: Selected Essays ofAbdus

Salam, 2nd ed., World Scientific, Singapore, p. 179-213.
[9] Fernando Espinoza (2005). "An analysis of the historical development of ideas about motion and its

implications for teaching", Physics Education 40 (2), p. 141.
[10] According to Maxwell in Matter and Motion, Newton meant by motion "the quantity of matter moved as well

as the rate at which it travels" and by impressed force he meant "the time during which the force acts as well as

the intensity of the force". See Harman and Shapiro, cited below.

Newton's laws of motion 114

[11] Plastino, Angel R. ; Muzzio, Juan C. (1992).

"http://articles.adsabs.harvard.edu//full/1992CeMDA..53..227P/0000227.000.html|On the use and abuse of
Newton's second law for variable mass problems" (in English). Celestial Mechanics and Dynamical Astronomy
(Netherlands: Kluwer Academic Publishers) vol. 53 (no. 3): pp. 227-232. ISSN 0923-2958 (http://worldcat.
org/issn/0923-2958). http://articles.adsabs.harvard.edu//full/1992CeMDA..53..227P/0000227.000.
html. Retrieved on 11 June 2009. "We may conclude emphasizing that Newton's second law is valid for constant
mass only. When the mass varies due to accretion or ablation, [an alternate eguation explicitly accounting for
the changing mass] should be used."

[12] Halliday; Resnick. Physics. 1. pp. 199. "It is important to note that we cannot derive a general expression for
Newton's second law for variable mass systems by treating the mass in F = dP/dt = d(Mv) as a variable. [...] We
can use F = dP/dt to analyze variable mass systems only if we apply it to an entire system of constant mass
having parts among which there is an interchange of mass." [Emphasis as in the original]

[13] Kleppner; Kolenkow. An Introduction to Mechanics, pp. 133-134. "Recall that F = dP/dt was established for a
system composed of a certain set of particles. ..it is essential to deal with the same set of particles throughout
the time interval... Conseguently, the mass of the system can not change during the time of interest."

[14] The use of algebraic expressions became popular during the 18th century, after Newton's death, while vector
notation dates to the late 19th century. The Principia expresses mathematical theorems in words and
consistently uses geometrical rather than algebraic proofs.

[15] I Bernard Cohen (Peter M. Harman & Alan E. Shapiro, Eds) (2002).

http://books. google. com/books?id=oYZ-0PUrjBcC&pg=PA353&dq=impulse+momentum+"rate+of+change"+-angular+date:20i
investigation of difficult things : essays on Newton and the history of the exact sciences in honour ofD.T.
Whiteside. Cambridge UK: Cambridge University Press, p. 353. ISBN 052189266X. http://books.google.com/
books?id=oYZ-0PUrjBcC&pg=PA353&dg=impulse+momentum+%22rate+of+change%22+-angular+
date:2000-2009&lr=&as_brr=0&sig=xM_5Q-nrbPkLLKcXAAbmogvVTcU.

[16] Hannah, J, Hillier, M J, Applied Mechanics, p221, Pitman Paperbacks, 1971

[17] Raymond A. Serway, Jerry S. Faughn (2006).

http://books. google. com/books?id=wDKD4IggBJ4C&pg=PA247&dq=impulse+momentum+"rate+of+change"&lr=&as_brr=0&t
Physics. Pacific Grove CA: Thompson-Brooks/Cole. p. 161. ISBN 0534997244. http://books.google.com/
books?id=wDKD4IggBJ4C&pg=PA247&dg=impulse+momentum+%22rate+of+change%22&lr=&
as_brr=0&sig=Up5LClE784npQuR21yDde6SetoQ#PPA161,Ml.

[18] WJ Stronge (2004).

http://books. google. com/books?id=nHgcS0bfZ28C&pg=PA12&dq-impulse+momentum+"rate+of+change"+-angular+date:20C
mechanics. Cambridge UK: Cambridge University Press, p. 12 ff. ISBN 0521602890. http://books.google.com/
books?id=nHgcS0bfZ28C&pg=PA12&dg=impulse+momentum+%22rate+of+change%22+-angular+
date:2000-2009&lr=&as_brr=0&sig=YVDmNVMz38AubS-51vRADvD2n6k.

[19] Newton, Principia, Corollary III to the laws of motion

Further reading

• Marion, Jerry and Thornton, Stephen. Classical Dynamics of Particles and Systems.
Harcourt College Publishers, 1995. ISBN 0-03-097302-3

• Fowles, G. R. and Cassiday, G. L. Analytical Mechanics (6ed). Saunders College
Publishing, 1999. ISBN 0-03-022317-2

• Feynman R P, Leighton R B & Sands M (2006).
http://worldcat.org/oclc/61355214&referer=brief_results\The Feynman lectures on
physics. Vol. 1. Pearson/Addison-Wesley. ISBN 0805390499. http://worldcat.org/oclc/
61 3552 14&referer=brief_results.

• Likins, Peter W. Elements of Engineering Mechanics McGraw-Hill Book Company, 1973.
ISBN 0-07-037852-5

Newton's laws of motion 115

External links

MIT Physics video lecture (http://academicearth.org/lectures/newtons-three-laws) on

Newton's three laws

Science aid: Newton's laws of motion (http://www.scienceaid.co.uk/physics/forces/

power.html)

Newtonian Physics (http://www.lightandmatter.com/html_books/lnp/ch04/ch04.

html) - an on-line textbook

Motion Mountain (http://www.motionmountain.net) - an on-line textbook (see also

Motion Mountain)

Newtonian attraction for three Planets (http://twt.mpei.ac.ru/MAS/Worksheets/

3_Planets.mcd) (Mathcad Application Server)

Gravity - Newton's Law for Kids (http://www.projectshum.org/Gravity/)

Simulation on Newton's first law of motion (http://phy.hk/wiki/englishhtm/firstlaw.

htm)

" Newton's Second Law (http://demonstrations.wolfram.com/NewtonsSecondLaw/)"

by Enrique Zeleny, Wolfram Demonstrations Project.

Analytical dynamics

In classical mechanics, analytical dynamics, or more briefly dynamics, is concerned
about the relationship between motion of bodies and its causes, namely the forces acting on
the bodies and the properties of the bodies (particularly mass and moment of inertia). The
foundation of modern day dynamics is Newtonian mechanics and its reformulation as
Lagrangian mechanics and Hamiltonian mechanics. The field has a long and important

history, as remarked by Hamilton:

The theoretical development of the laws of motion of bodies is a problem of such
interest and importance that it has engaged the attention of all the eminent
mathematicians since the invention of the dynamics as a mathematical science by
Galileo, and especially since the wonderful extension which was given to that science
by Newton

- William Rowan Hamilton, 1834 (Transcribed in Classical Mechanics byJ.R. Taylor, p.

237 [3] )

Some authors (for example, Taylor (2005) ^ and Greenwood (1997) [ ] ) include special
relativity within classical dynamics.

Relationship to static s, kinetics, and kinematics

Historically, there were three branches of classical mechanics: "statics" (the study of
equilibrium and its relation to forces); "kinetics" (the study of motion and its relation to
forces) and "kinematics" (dealing with the implications of observed motions without
regard for circumstances causing them). These three subjects have been connected to
dynamics in several ways. One approach combined statics and kinetics under the name
dynamics, which became the branch dealing with determination of the motion of bodies

T71

resulting from the action of specified forces ; another approach separated statics, and
combined kinetics and kinematics under the rubric dynamics. This approach is

common in engineering books on mechanics, and is still in widespread use among

Analytical dynamics 116

mechanicians.

Fundamental importance in engineering, diminishing emphasis in
physics

Today, dynamics and kinematics continue to be considered the two pillars of classical
mechanics. Dynamics is still included in mechanical, aerospace, and other engineering
curriculums because of its importance in machine design, the design of land, sea, air, and
space vehicles and other applications. However, few modern physicists concern themselves
with an independent treatment of "dynamics" or "kinematics", nevermind "statics" or
"kinetics". Instead, the entire undifferentiated subject is referred to as classical mechanics.
In fact, many undergraduate and graduate text books since mid-2 Oth century on "classical

mechanics" lack chapters titled "dynamics" or "kinematics" . [3] [10] [11] [12] [13] [14] [15] [16]

ri7i

In these books, although the word "dynamics" is used when acceleration is ascribed to a

force, the word "kinetics" is never mentioned. However, clear exceptions exist. Prominent

MO]

examples include The Feynman Lectures on Physics.

Fundamental Principles

• Newton's laws of motion

• Inertia

• Acceleration

• Momentum

• Reaction

• Newton's law of universal gravitation

• Special theory of relativity

Axioms and mathematical treatments

• Variational principles and Lagrange's equations

• Hamilton's equations

• Canonical transformations

• Hamilton-Jacobi Theory

Related engineering branches

• Particle dynamics

• Rigid body dynamics

• Soft body dynamics

• Fluid dynamics

• Hydrodynamics

• Gas dynamics

• Aerodynamics

Analytical dynamics 117

Related subjects

• Statics

References

[I] Chris Doran, Anthony N. Lasenby (2003).

http://books. google. com/books?id=VW4yt0WHdjoC&pg=PA54&dq=classical+dynamics+-quantum+date:2002-2009&lr=&as_bi
Algebra for Physicists. Cambridge University Press, p. p. 54. ISBN 0521480221. http://books.google.com/
books?id=VW4yt0WHdjoC&pg=PA54&dq=classical+dynamics+-guantum+date:2002-2009&lr=&
as_brr=0&sig=ACfU3UllsyztEgIW0cnsvMxQhOlnQ51KRw.

[2] Cornelius Lanczos (1986).

http://books.google.com/books?id=ZWoYYr8wk2IC&pg=PR4&dq=isbn=0486650677&sig=ACfU3U2R5sLjGS22S-h8ZJ9RiPJnKi
variational principles of mechanics (Reprint of 4th Edition of 1970 ed.). Dover Publications Inc.. p. pp. 5-6. ISBN
0-486-65067-7. http://books. google. com/books?id=ZWoYYr8wk2IC&pg=PR4&dq=isbn=0486650677&
sig=ACfU3U2R5sLjGS22S-h8Zj9RiPJnKcKZg#PPA5,Ml.

[3] John Robert Taylor (2005). http://books.google.com/books?id-PlkCtNr-pJsC&q-dynamics#search\Classical
Mechanics. University Science Books. ISBN 189138922X, 9781891389221. http://books.google.com/
books?id=PlkCtNr-pJsC&q=dynamics#search.

[4] Donald T Greenwood (1997).

http-./fbooks. google. com/books?id=x7rj83I98yMC&printsec=frontcover&dq-classical+dynamics&lr-&as_brr-0&sig=ACfU3U2
Mechanics (Reprint of 1977 ed.). Courier Dover Publications, p. p. 1. ISBN 0486696901. http://books. google.
com/books?id=x7rj83I98yMC&printsec=frontcover&dq=classical+dynamics&lr=&as_brr=0&
sig=ACfU3U2-bllzGZZqchuPzO_7Pu7IF-5UyQ#PPAl,Ml.

[5] Thomas Wallace Wright (1896).

http://books. google. com/books?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics&lr=&as_brr=0#PPA85,Ml \l
of Mechanics Including Kinematics, Kinetics and Statics: with applications. E. and F. N. Spon. p. p. 85. http://
books, google. com/books?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics&lr=&
as_brr=0#PPA85,Ml.

[6] Edmund Taylor Whittaker (1988).

http-./fbooks. google. com/books?id=epHlhCB7N2MC&printsec=frontcover&dq=inauthor:"E+T+Whittaker"&lr=&as_brr=0&sig

Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three

Bodies (Fourth edition of 1936 with foreword by Sir William McCrea ed.). Cambridge University Press.

p. Chapter 1, p. 1. ISBN 0521358833. http://books. google. com/books?id=epHlhCB7N2MC&

printsec=frontcover&dq=inauthor:%22E+T+Whittaker%22&lr=&as_brr=0&

sig=SN7_oYmNYM4QRSgjULXBU5jeQrA&source=gbs_book_other_versions_r&cad=0_2#PPAl,Ml.

[7] James Gordon MacGregor (1887).

http://books. google. com/books?id=3yMQAAAAYAAJ&printsec=frontcover&dq=kinematics+dynamics&lr=&as_brr=0#PPR5,Ml
Elementary Treatise on Kinematics and Dynamics. Macmillan. p. p. v. http://books.google.com/
books?id=3yMQAAAAYAAJ&printsec=frontcover&dq=kinematics+dynamics&lr=&as_brr=0#PPR5,Ml.

[8] Stephen Timoshenko, Donovan Harold Young (1956).

http://books. google. ca/books?id=I548AAAAIAAJ&q=engineering+mechanics+inauthor:Timoshenko&dq=engineering+mechanii
mechanics. McGraw Hill. http://books. google. ca/books?id=I548AAAAIAAJ&q=engineering+mechanics+
inauthor:Timoshenko&dq=engineering+mechanics+inauthor:Timoshenko&lr=&as_brr=0&
ei=hX_SS02_E432sgPuzrGTBw&pgis=l.

[9] Lakshmana C. Rao, J. Lakshminarasimhan, Raju Sethuraman, Srinivasan M. Sivakumar (2004).

http://books. google. com/books?id=F7gaalShPKIC&printsec=frontcover&dq=statics+dynamics&lr-&as_brr-0&sig=ACfU3U2l
mechanics. PHI Learning Pvt. Ltd.. p. p. vz. ISBN 8120321898. http://books.google.com/
books?id=F7gaalShPKIC&printsec=frontcover&dq=statics+dynamics&lr=&as_brr=0&
sig=ACfU3U2haQ0TLc90YwYiTtuhvIgfA6ZXEQ#PPR6,Ml.

[10] David Hestenes (1999).

http://books. google. com/books?id=eU2qm8wavRwC&pg=PA198&dq=dynamics+kinematics&lr=&as_brr=0&sig -AC fU3U2C3a
Foundations for Classical Mechanics. Springer, p. p. 198. ISBN 0792355148. http://books.google.com/
books?id=eU2qm8wavRwC&pg=PA198&dq=dynamics+kinematics&lr=&as_brr=0&
sig=ACfU3U2C3aW_zumPCy2Doe4K4NKsjJXKeQ.

[II] R. Douglas Gregory (2006).
http://books.google.com/books?id=uAfUQmQbzOkC&q=dynamics#search\Classical Mechanics: An
Undergraduate Text. Cambridge University Press. ISBN 0521826780, 9780521826785. http://books. google.
com/books?id=uAfUQmQbzOkC&q=dynamics#search.

Analytical dynamics 118

[12] Landau, L. D.; Lifshitz, E. M. ; Sykes, J.B.; Bell, J. S. (1976),

http://books.google.com/books?id=LmAV8q_OOOgC\Mechanics, 1, Butterworth-Heinemann, ISBN 0750628960,

9780750628969, http://books.google.com/books?id=LmAV8q_OOOgC
[13] Jorge Valenzuela Jose, Eugene Jerome Saletan (1998).

http-./fbooks. google. com/books?id-ZW0L5Xe9zhwC\Classical Dynamics: A Contemporary Approach. Cambridge

University Press. ISBN 0521636361, 9780521636360. http://books. google. com/books?id=ZW0L5Xe9zhwC.
[14] T. W. B. Kibble, Frank H. Berkshire (2004). http-.//books.google.com/books?id=0a8dk0eDxgEC\Classical

Mechanics. Imperial College Press. ISBN 1860944353, 9781860944352. http://books.google.com/

books?id=0a8dk0eDxgEC.
[15] Walter Greiner, S. Allan Bromley (2003). http://books.google.com/books?id=L_APSPGoI5sC\Classical

Mechanics: Point Particles and Relativity. Springer. ISBN 0387955860, 9780387955865. http://books. google.

com/books?id=L_APSPGoI5sC.
[16] Gerald Jay Sussman, Jack Wisdom Meinhard, Edwin Mayer (2001).

http://books. google. com/books?client= fire fox-a&id=H_6Ux04cPv8C&q=dynamics#search\Structure and

Interpretation of Classical Mechanics. MIT Press. ISBN 0262194554, 9780262194556. http://books. google.

com/books?client=firefox-a&id=H_6Ux04cPv8C&q=dynamics#search.
[17] Harald Iro (2002). http://books.google.com/books?id=-L5ckgdxA5YC\A Modern Approach to Classical

Mechanics. World Scientific. ISBN 9812382135, 9789812382139. http://books.google.com/

books?id=-L5ckgdxA5YC.
[18] Feynman, RP; Leighton, RB; Sands, M (2003), The Feynman Lectures on Physics, Vol. 1 (Reprint of 1963

lectures ed.), Perseus Books Group, p. Ch. 9 Newton's Laws of Dynamics, ISBN 0738209309

Molecular dynamics

Molecular dynamics (MD) is a form of computer simulation in which atoms and molecules
are allowed to interact for a period of time by approximations of known physics, giving a
view of the motion of the atoms. Because molecular systems generally consist of a vast
number of particles, it is impossible to find the properties of such complex systems
analytically. When the number of bodies are more than two no analytical solutions can be
found and result in chaotic motion (see n-body problem). MD simulation circumvents this
problem by using numerical methods. It represents an interface between laboratory
experiments and theory, and can be understood as a "virtual experiment". MD probes the
relationship between molecular structure, movement and function. Molecular dynamics is a
multidisciplinary method. Its laws and theories stem from mathematics, physics, and

chemistry, and it employs algorithms from computer science and information theory. It was

rn r2i

originally conceived within theoretical physics in the late 1950s and early 1960s , but

is applied today mostly in materials science and modeling of biomolecules.

Before it became possible to simulate molecular dynamics with computers, some undertook
the hard work of trying it with physical models such as macroscopic spheres. The idea was
to arrange them to replicate the properties of a liquid. J.D. Bernal said, in 1962: "... I took a
number of rubber balls and stuck them together with rods of a selection of different lengths
ranging from 2.75 to 4 inches. I tried to do this in the first place as casually as possible,
working in my own office, being interrupted every five minutes or so and not remembering

T31

what I had done before the interruption." Fortunately, now computers keep track of
bonds during a simulation.

Molecular dynamics is a specialized discipline of molecular modeling and computer
simulation based on statistical mechanics; the main justification of the MD method is that
statistical ensemble averages are equal to time averages of the system, known as the
ergodic hypothesis. MD has also been termed "statistical mechanics by numbers" and
"Laplace's vision of Newtonian mechanics" of predicting the future by animating nature's

Molecular dynamics

119

forces' ] [ ] and allowing insight into molecular motion on an atomic scale. However, long
MD simulations are mathematically ill-conditioned, generating cumulative errors in
numerical integration that can be minimized with proper selection of algorithms and
parameters, but not eliminated entirely. Furthermore, current potential functions are, in
many cases, not sufficiently accurate to reproduce the dynamics of molecular systems, so
the much more computationally demanding Ab Initio Molecular Dynamics method must be
used. Nevertheless, molecular dynamics techniques allow detailed time and space
resolution into representative behavior in phase space.

Give atoms initial positions f'- - 1 , choose short At
1

Get forces F - - V V(r®) and a - F/m

Move atoms: r«* 1 > = r"> +v« At + V? a At 2 +

Move time forward: t = t + At

Repeat as long as you need

Highly simplified description of the molecular dynamics simulation

algorithm. The simulation proceeds iteratively by alternatively

calculating forces and solving the equations of motion based on the

accelerations obtained from the new forces. In practise, almost all

MD codes use much more complicated versions of the algorithm,

including two steps (predictor and corrector) in solving the equations

of motion and many additional steps for e.g. temperature and

pressure control, analysis and output.

Areas of Application

There is a significant difference
between the focus and methods
used by chemists and
physicists, and this is reflected
in differences in the jargon
used by the different fields. In
chemistry and biophysics, the
interaction between the
particles is either described by
a "force field" (classical MD),
a quantum chemical model, or
a mix between the two. These
terms are not used in physics,
where the interactions are
usually described by the name
of the theory or approximation
being used and called the
potential energy, or just "potential".

Beginning in theoretical physics, the method of MD gained popularity in materials science
and since the 1970s also in biochemistry and biophysics. In chemistry, MD serves as an
important tool in protein structure determination and refinement using experimental tools
such as X-ray crystallography and NMR. It has also been applied with limited success as a
method of refining protein structure predictions. In physics, MD is used to examine the
dynamics of atomic-level phenomena that cannot be observed directly, such as thin film
growth and ion-subplantation. It is also used to examine the physical properties of
nanotechnological devices that have not or cannot yet be created.

In applied mathematics and theoretical physics, molecular dynamics is a part of the
research realm of dynamical systems, ergodic theory and statistical mechanics in general.
The concepts of energy conservation and molecular entropy come from thermodynamics.
Some techniques to calculate conformational entropy such as principal components analysis
come from information theory. Mathematical techniques such as the transfer operator
become applicable when MD is seen as a Markov chain. Also, there is a large community of
mathematicians working on volume preserving, symplectic integrators for more
computationally efficient MD simulations.

Molecular dynamics 120

MD can also be seen as a special case of the discrete element method (DEM) in which the
particles have spherical shape (e.g. with the size of their van der Waals radii.) Some
authors in the DEM community employ the term MD rather loosely, even when their
simulations do not model actual molecules.

Design Constraints

Design of a molecular dynamics simulation should account for the available computational
power. Simulation size (n=number of particles), timestep and total time duration must be
selected so that the calculation can finish within a reasonable time period. However, the
simulations should be long enough to be relevant to the time scales of the natural processes
being studied. To make statistically valid conclusions from the simulations, the time span
simulated should match the kinetics of the natural process. Otherwise, it is analogous to
making conclusions about how a human walks from less than one footstep. Most scientific
publications about the dynamics of proteins and DNA use data from simulations spanning
nanoseconds (1E-9 s) to microseconds (1E-6 s). To obtain these simulations, several
CPU-days to CPU-years are needed. Parallel algorithms allow the load to be distributed
among CPUs; an example is the spatial decomposition in LAMMPS.

During a classical MD simulation, the most CPU intensive task is the evaluation of the
potential (force field) as a function of the particles' internal coordinates. Within that energy
evaluation, the most expensive one is the non-bonded or non-covalent part. In Big O
notation, common molecular dynamics simulations scale by 0{n )if all pair-wise
electrostatic and van der Waals interactions must be accounted for explicitly. This
computational cost can be reduced by employing electrostatics methods such as Particle
Mesh Ewald ( 0(nlog(n))) or good spherical cutoff techniques ( 0(n)).

Another factor that impacts total CPU time required by a simulation is the size of the
integration timestep. This is the time length between evaluations of the potential. The
timestep must be chosen small enough to avoid discretization errors (i.e. smaller than the
fastest vibrational frequency in the system). Typical timesteps for classical MD are in the
order of 1 femtosecond (1E-15 s). This value may be extended by using algorithms such as
SHAKE, which fix the vibrations of the fastest atoms (e.g. hydrogens) into place. Multiple
time scale methods have also been developed, which allow for extended times between
updates of slower long-range forces.

For simulating molecules in a solvent, a choice should be made between explicit solvent and
implicit solvent. Explicit solvent particles (such as the TIP3P and SPC/E water models) must
be calculated expensively by the force field, while implicit solvents use a mean-field
approach. Using an explicit solvent is computationally expensive, requiring inclusion of
about ten times more particles in the simulation. But the granularity and viscosity of
explicit solvent is essential to reproduce certain properties of the solute molecules. This is
especially important to reproduce kinetics.

In all kinds of molecular dynamics simulations, the simulation box size must be large
enough to avoid boundary condition artifacts. Boundary conditions are often treated by
choosing fixed values at the edges, or by employing periodic boundary conditions in which
one side of the simulation loops back to the opposite side, mimicking a bulk phase.

Molecular dynamics 121

Microcanonical ensemble (NVE)

In the microcanonical, or NVE ensemble, the system is isolated from changes in moles
(N), volume (V) and energy (E). It corresponds to an adiabatic process with no heat
exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of
potential and kinetic energy, with total energy being conserved. For a system of N particles
with coordinates A' and velocities V, the following pair of first order differential equations
may be written in Newton's notation as

F{X) = -W(X) = MV(t)

V(t) = X(t).
The potential energy function &{X) of the system is a function of the particle coordinates
X . It is referred to simply as the "potential" in Physics, or the "force field" in Chemistry.
The first equation comes from Newton's laws; the force i^acting on each particle in the
system can be calculated as the negative gradient of k r (A") .

For every timestep, each particle's position A' and velocity I 'may be integrated with a
symplectic method such as Verlet. The time evolution of A' and Vis called a trajectory.
Given the initial positions (e.g. from theoretical knowledge) and velocities (e.g. randomized
Gaussian), we can calculate all future (or past) positions and velocities.

One frequent source of confusion is the meaning of temperature in MD. Commonly we have
experience with macroscopic temperatures, which involve a huge number of particles. But
temperature is a statistical quantity. If there is a large enough number of atoms, statistical
temperature can be estimated from the instantaneous temperature, which is found by
equating the kinetic energy of the system to nk T/2 where n is the number of degrees of
freedom of the system.

A temperature-related phenomenon arises due to the small number of atoms that are used
in MD simulations. For example, consider simulating the growth of a copper film starting
with a substrate containing 500 atoms and a deposition energy of 100 eV. In the real world,
the 100 eV from the deposited atom would rapidly be transported through and shared
among a large number of atoms ( 10 1Cl or more) with no big change in temperature. When
there are only 500 atoms, however, the substrate is almost immediately vaporized by the
deposition. Something similar happens in biophysical simulations. The temperature of the
system in NVE is naturally raised when macromolecules such as proteins undergo
exothermic conformational changes and binding.

Canonical ensemble (NVT)

In the canonical ensemble, moles (N), volume (V) and temperature (T) are conserved. It is
also sometimes called constant temperature molecular dynamics (CTMD). In NVT, the
energy of endothermic and exothermic processes is exchanged with a thermostat.

A variety of thermostat methods are available to add and remove energy from the
boundaries of an MD system in a realistic way, approximating the canonical ensemble.
Popular techniques to control temperature include the Nose-Hoover thermostat, the
Berendsen thermostat, and Langevin dynamics. Note that the Berendsen thermostat might
introduce the flying ice cube effect, which leads to unphysical translations and rotations of
the simulated system.

Molecular dynamics 122

Isothermal-Isobaric (NPT) ensemble

In the isothermal-isobaric ensemble, moles (N), pressure (P) and temperature (T) are
conserved. In addition to a thermostat, a barostat is needed. It corresponds most closely to
laboratory conditions with a flask open to ambient temperature and pressure.

In the simulation of biological membranes, isotropic pressure control is not appropriate.
For lipid bilayers, pressure control occurs under constant membrane area (NPAT) or
constant surface tension "gamma" (NPyT).

Generalized ensembles

The replica exchange method is a generalized ensemble. It was originally created to deal
with the slow dynamics of disordered spin systems. It is also called parallel tempering. The
replica exchange MD (REMD) formulation tries to overcome the multiple-minima

problem by exchanging the temperature of non-interacting replicas of the system running
at several temperatures.

Potentials in MD simulations

A molecular dynamics simulation requires the definition of a potential function, or a
description of the terms by which the particles in the simulation will interact. In chemistry
and biology this is usually referred to as a force field. Potentials may be defined at many
levels of physical accuracy; those most commonly used in chemistry are based on molecular
mechanics and embody a classical treatment of particle-particle interactions that can
reproduce structural and conformational changes but usually cannot reproduce chemical
reactions.

The reduction from a fully quantum description to a classical potential entails two main
approximations. The first one is the Born-Oppenheimer approximation, which states that
the dynamics of electrons is so fast that they can be considered to react instantaneously to
the motion of their nuclei. As a consequence, they may be treated separately. The second
one treats the nuclei, which are much heavier than electrons, as point particles that follow
classical Newtonian dynamics. In classical molecular dynamics the effect of the electrons is
approximated as a single potential energy surface, usually representing the ground state.

When finer levels of detail are required, potentials based on quantum mechanics are used;
some techniques attempt to create hybrid classical/quantum potentials where the bulk of
the system is treated classically but a small region is treated as a quantum system, usually
undergoing a chemical transformation.

Empirical potentials

Empirical potentials used in chemistry are frequently called force fields, while those used in
materials physics are called just empirical or analytical potentials.

Most force fields in chemistry are empirical and consist of a summation of bonded forces
associated with chemical bonds, bond angles, and bond dihedrals, and non-bonded forces
associated with van der Waals forces and electrostatic charge. Empirical potentials
represent quantum-mechanical effects in a limited way through ad-hoc functional
approximations. These potentials contain free parameters such as atomic charge, van der
Waals parameters reflecting estimates of atomic radius, and equilibrium bond length,
angle, and dihedral; these are obtained by fitting against detailed electronic calculations

Molecular dynamics 123

(quantum chemical simulations) or experimental physical properties such as elastic
constants, lattice parameters and spectroscopic measurements.

Because of the non-local nature of non-bonded interactions, they involve at least weak
interactions between all particles in the system. Its calculation is normally the bottleneck in
the speed of MD simulations. To lower the computational cost, force fields employ
numerical approximations such as shifted cutoff radii, reaction field algorithms, particle
mesh Ewald summation, or the newer Particle-Particle Particle Mesh (P3M).

Chemistry force fields commonly employ preset bonding arrangements (an exception being
ab-initio dynamics), and thus are unable to model the process of chemical bond breaking
and reactions explicitly. On the other hand, many of the potentials used in physics, such as
those based on the bond order formalism can describe several different coordinations of a
system and bond breaking. Examples of such potentials include the Brenner potential for

hydrocarbons and its further developments for the C-Si-H and C-O-H systems. The ReaxFF
potential can be co
chemistry force fields.

rm
potential can be considered a fully reactive hybrid between bond order potentials and

Pair potentials vs. many-body potentials

The potential functions representing the non-bonded energy are formulated as a sum over
interactions between the particles of the system. The simplest choice, employed in many
popular force fields, is the "pair potential", in which the total potential energy can be
calculated from the sum of energy contributions between pairs of atoms. An example of
such a pair potential is the non-bonded Lennard -Jones potential (also known as the 6-12
potential), used for calculating van der Waals forces.

U(r) = ie

r-(*r

Another example is the Born (ionic) model of the ionic lattice. The first term in the next
equation is Coulomb's law for a pair of ions, the second term is the short-range repulsion
explained by Pauli's exclusion principle and the final term is the dispersion interaction
term. Usually, a simulation only includes the dipolar term, although sometimes the
quadrupolar term is included as well.

%(^) = E 5rr + E A ex P =-p> + E <W + ■ ■ ■

In many-body potentials, the potential energy includes the effects of three or more particles
interacting with each other. In simulations with pairwise potentials, global interactions in
the system also exist, but they occur only through pairwise terms. In many-body potentials,
the potential energy cannot be found by a sum over pairs of atoms, as these interactions are
calculated explicitly as a combination of higher-order terms. In the statistical view, the

dependency between the variables cannot in general be expressed using only pairwise

ri2i
products of the degrees of freedom. For example, the Tersoff potential , which was

originally used to simulate carbon, silicon and germanium and has since been used for a

wide range of other materials, involves a sum over groups of three atoms, with the angles

between the atoms being an important factor in the potential. Other examples are the

ri3i
embedded-atom method (EAM) and the Tight-Binding Second Moment Approximation

(TBSMA) potentials , where the electron density of states in the region of an atom is

calculated from a sum of contributions from surrounding atoms, and the potential energy

contribution is then a function of this sum.

Molecular dynamics 124

Semi-empirical potentials

Semi-empirical potentials make use of the matrix representation from quantum mechanics.
However, the values of the matrix elements are found through empirical formulae that
estimate the degree of overlap of specific atomic orbitals. The matrix is then diagonalized to
determine the occupancy of the different atomic orbitals, and empirical formulae are used
once again to determine the energy contributions of the orbitals.

There are a wide variety of semi-empirical potentials, known as tight-binding potentials,
which vary according to the atoms being modeled.

Polarizable potentials

Most classical force fields implicitly include the effect of polarizability, e.g. by scaling up
the partial charges obtained from quantum chemical calculations. These partial charges are
stationary with respect to the mass of the atom. But molecular dynamics simulations can
explicitly model polarizability with the introduction of induced dipoles through different
methods, such as Drude particles or fluctuating charges. This allows for a dynamic
redistribution of charge between atoms which responds to the local chemical environment.

For many years, polarizable MD simulations have been touted as the next generation. For
homogenous liquids such as water, increased accuracy has been achieved through the
inclusion of polarizability. Some promising results have also been achieved for

proteins. However, it is still uncertain how to best approximate polarizability in a
simulation.

Ab-initio methods

In classical molecular dynamics, a single potential energy surface (usually the ground state)
is represented in the force field. This is a consequence of the Born-Oppenheimer
approximation. If excited states, chemical reactions or a more accurate representation is
needed, electronic behavior can be obtained from first principles by using a quantum
mechanical method, such as Density Functional Theory. This is known as Ab Initio
Molecular Dynamics (AIMD). Due to the cost of treating the electronic degrees of freedom,
the computational cost of this simulations is much higher than classical molecular
dynamics. This implies that AIMD is limited to smaller systems and shorter periods of time.

Ab-initio quantum-mechanical methods may be used to calculate the potential energy of a
system on the fly, as needed for conformations in a trajectory. This calculation is usually
made in the close neighborhood of the reaction coordinate. Although various
approximations may be used, these are based on theoretical considerations, not on
empirical fitting. Ab-initio calculations produce a vast amount of information that is not
available from empirical methods, such as density of electronic states or other electronic
properties. A significant advantage of using ab-initio methods is the ability to study
reactions that involve breaking or formation of covalent bonds, which correspond to
multiple electronic states.

A popular software for ab-initio molecular dynamics is the Car-Parrinello Molecular
Dynamics (CPMD) package based on the density functional theory.

Molecular dynamics 125

Hybrid QM/MM

QM (quantum-mechanical) methods are very powerful. However, they are computationally
expensive, while the MM (classical or molecular mechanics) methods are fast but suffer
from several limitations (require extensive parameterization; enerqy estimates obtained are
not very accurate; cannot be used to simulate reactions where covalent bonds are
broken/formed; and are limited in their abilities for providinq accurate details reqardinq the
chemical environment). A new class of method has emerqed that combines the qood points
of QM (accuracy) and MM (speed) calculations. These methods are known as mixed or
hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM). The
methodoloqy for such techniques was introduced by Warshel and coworkers. In the recent
years have been pioneered by several qroups includinq: Arieh Warshel (University of
Southern California), Weitao Yanq (Duke University), Sharon Hammes-Schiffer (The
Pennsylvania State University), Donald Truhlar and Jiali Gao (University of Minnesota) and
Kenneth Merz (University of Florida).

The most important advantaqe of hybrid QM/MM methods is the speed. The cost of doinq
classical molecular dynamics (MM) in the most straiqhtforward case scales 0(n ), where N
is the number of atoms in the system. This is mainly due to electrostatic interactions term
(every particle interacts with every other particle). However, use of cutoff radius, periodic
pair-list updates and more recently the variations of the particle-mesh Ewald's (PME)
method has reduced this between O(N) to 0(n ). In other words, if a system with twice
many atoms is simulated then it would take between twice to four times as much computinq
power. On the other hand the simplest ab-initio calculations typically scale 0(n ) or worse

2 7

(Restricted Hartree-Fock calculations have been suqqested to scale ~0(n ' )). To overcome
the limitation, a small part of the system is treated quantum-mechanically (typically
active-site of an enzyme) and the remaininq system is treated classically.

In more sophisticated implementations, QM/MM methods exist to treat both liqht nuclei
susceptible to quantum effects (such as hydroqens) and electronic states. This allows
qeneration of hydroqen wave-functions (similar to electronic wave-functions). This
methodoloqy has been useful in investiqatinq phenomenon such as hydroqen tunnelinq. One
example where QM/MM methods have provided new discoveries is the calculation of

hydride transfer in the enzyme liver alcohol dehydroqenase. In this case, tunnelinq is

ri7i
important for the hydroqen, as it determines the reaction rate.

Coarse-graining and reduced representations

At the other end of the detail scale are coarse-qrained and lattice models. Instead of
explicitly representinq every atom of the system, one uses "pseudo-atoms" to represent
qroups of atoms. MD simulations on very larqe systems may require such larqe computer
resources that they cannot easily be studied by traditional all-atom methods. Similarly,
simulations of processes on lonq timescales (beyond about 1 microsecond) are prohibitively
expensive, because they require so many timesteps. In these cases, one can sometimes
tackle the problem by usinq reduced representations, which are also called coarse-qrained
models.

Examples for coarse qraininq (CG) methods are discontinuous molecular dynamics

r 1 si r 1 qi r9oi

(CG-DMD) and Go-models . Coarse-qraininq is done sometimes takinq larqer

pseudo-atoms. Such united atom approximations have been used in MD simulations of

bioloqical membranes. The aliphatic tails of lipids are represented by a few pseudo-atoms

Molecular dynamics 126

by gathering 2-4 methylene groups into each pseudo-atom.

The parameterization of these very coarse-grained models must be done empirically, by
matching the behavior of the model to appropriate experimental data or all-atom
simulations. Ideally, these parameters should account for both enthalpic and entropic
contributions to free energy in an implicit way. When coarse-graining is done at higher
levels, the accuracy of the dynamic description may be less reliable. But very
coarse-grained models have been used successfully to examine a wide range of questions in
structural biology.

Examples of applications of coarse-graining in biophysics:

• protein folding studies are often carried out using a single (or a few) pseudo-atoms per
amino acid;

• DNA supercoiling has been investigated using 1-3 pseudo-atoms per basepair, and at
even lower resolution;

• Packaging of double-helical DNA into bacteriophage has been investigated with models
where one pseudo-atom represents one turn (about 10 basepairs) of the double helix;

• RNA structure in the ribosome and other large systems has been modeled with one
pseudo-atom per nucleotide.

The simplest form of coarse-graining is the "united atom" (sometimes called "extended
atom") and was used in most early MD simulations of proteins, lipids and nucleic acids. For
example, instead of treating all four atoms of a CH methyl group explicitly (or all three
atoms of CH methylene group), one represents the whole group with a single pseudo-atom.
This pseudo-atom must, of course, be properly parameterized so that its van der Waals
interactions with other groups have the proper distance-dependence. Similar
considerations apply to the bonds, angles, and torsions in which the pseudo-atom
participates. In this kind of united atom representation, one typically eliminates all explicit
hydrogen atoms except those that have the capability to participate in hydrogen bonds
("polar hydrogens"). An example of this is the Charmm 19 force-field.

The polar hydrogens are usually retained in the model, because proper treatment of
hydrogen bonds requires a reasonably accurate description of the directionality and the
electrostatic interactions between the donor and acceptor groups. A hydroxyl group, for
example, can be both a hydrogen bond donor and a hydrogen bond acceptor, and it would
be impossible to treat this with a single OH pseudo-atom. Note that about half the atoms in
a protein or nucleic acid are nonpolar hydrogens, so the use of united atoms can provide a
substantial savings in computer time.

Examples of applications

Molecular dynamics is used in many fields of science.

• First macromolecular MD simulation published (1977, Size: 500 atoms, Simulation Time:
9.2 ps=0.0092 ns, Program: CHARMM precursor) Protein: Bovine Pancreatic Trypsine
Inhibitor. This is one of the best studied proteins in terms of folding and kinetics. Its
simulation published in Nature magazine paved the way for understanding protein
motion as essential in function and not just accessory.

• MD is the standard method to treat collision cascades in the heat spike regime, i.e. the

["221 r 2 3 1

effects that energetic neutron and ion irradiation have on solids an solid surfaces.

Molecular dynamics 127

The following two biophysical examples are not run-of-the-mill MD simulations. They
illustrate almost heroic efforts to produce simulations of a system of very large size (a
complete virus) and very long simulation times (500 microseconds):

• MD simulation of the complete satellite tobacco mosaic virus (STMV) (2006, Size: 1
million atoms, Simulation time: 50 ns, program: NAMD) This virus is a small, icosahedral
plant virus which worsens the symptoms of infection by Tobacco Mosaic Virus (TMV).
Molecular dynamics simulations were used to probe the mechanisms of viral assembly.
The entire STMV particle consists of 60 identical copies of a single protein that make up
the viral capsid (coating), and a 1063 nucleotide single stranded RNA genome. One key
finding is that the capsid is very unstable when there is no RNA inside. The simulation
would take a single 2006 desktop computer around 35 years to complete. It was thus
done in many processors in parallel with continuous communication between them. ^

• Folding Simulations of the Villin Headpiece in All-Atom Detail (2006, Size: 20,000 atoms;
Simulation time: 500 us = 500,000 ns, Program: folding@home) This simulation was run
in 200,000 CPU's of participating personal computers around the world. These
computers had the folding@home program installed, a large-scale distributed computing
effort coordinated by Vijay Pande at Stanford University. The kinetic properties of the
Villin Headpiece protein were probed by using many independent, short trajectories run
by CPU's without continuous real-time communication. One technique employed was the
Pfold value analysis, which measures the probability of folding before unfolding of a
specific starting conformation. Pfold gives information about transition state structures
and an ordering of conformations along the folding pathway. Each trajectory in a Pfold
calculation can be relatively short, but many independent trajectories are needed.

Molecular dynamics algorithms
Integrators

• Verlet-Stoermer integration

• Runge-Kutta integration

• Beeman's algorithm

• Gear predictor - corrector

• Constraint algorithms (for constrained systems)

• Symplectic integrator

Short-range interaction algorithms

• Cell lists

• Verlet list

• Bonded interactions

Long-range interaction algorithms

• Ewald summation

• Particle Mesh Ewald (PME)

• Particle-Particle Particle Mesh P3M

• Reaction Field Method

Molecular dynamics 128

Parallelization strategies

• Domain decomposition method (Distribution of system data for parallel computing)

• Molecular Dynamics - Parallel Algorithms

Major software for MD simulations

Abalone (classical, implicit water)

ABINIT (DFT)

ACEMD [3] (running on NVIDIA GPUs: heavily optimized with CUDA)

T271

ADUN (classical, P2P database for simulations)

AMBER (classical)

Ascalaph (classical, GPU accelerated)

CASTEP (DFT)

CPMD (DFT)

CP2K [29] (DFT)

CHARMM (classical, the pioneer in MD simulation, extensive analysis tools)

COSMOS (classical and hybrid QM/MM, quantum-mechanical atomic charges with

BPT)

Desmond (classical, parallelization with up to thousands of CPU's)

DL_POLY [31] (classical)

ESPResSo (classical, coarse-grained, parallel, extensible)

Fireball [32] (tight-binding DFT)

GROMACS (classical)

GROMOS (classical)

GULP (classical)

Hippo [33] (classical)

LAMMPS (classical, large-scale with spatial-decomposition of simulation domain for

parallelism)

MDynaMix (classical, parallel)

MOLDY [25] (classical, parallel) latest release [34]

Materials Studio [17] (Forcite MD using COMPASS, Dreiding, Universal, cvff and pcff

forcefields in serial or parallel, QMERA (QM+MD), ONESTEP (DFT), etc.)

MOSCITO (classical)

NAMD (classical, parallelization with up to thousands of CPU's)

NEWTON-X (ab initio, surface-hopping dynamics)

ProtoMol (classical, extensible, includes multigrid electrostatics)

PWscf (DFT)

S/PHI/nX [37] (DFT)

SIESTA (DFT)

VASP (DFT)

TINKER (classical)

YASARA [38] (classical)

ORAC [39] (classical)

XMD (classical)

Molecular dynamics 129

Related software

• VMD - MD simulation trajectories can be visualized and analyzed.

• PyMol - Molecular Visualization software written in python

• Packmol Package for building starting configurations for MD in an automated fashion

• Sirius - Molecular modeling, analysis and visualization of MD trajectories

• esra - Lightweight molecular modeling and analysis library
(Java/Jython/Mathematica).

• Molecular Workbench - Interactive molecular dynamics simulations on your desktop

• BOSS - MC in OPLS

Specialized hardware for MD simulations

• Anton - A specialized, massively parallel supercomputer designed to execute MD
simulations.

• MDGRAPE - A special purpose system built for molecular dynamics simulations,
especially protein structure prediction.

See also

Molecular graphics

Molecular modeling

Computational chemistry

Energy drift

Force field in Chemistry

Force field implementation

Monte Carlo method

Molecular Design software

Molecular mechanics

Molecular modeling on GPU

Protein dynamics

Implicit solvation

Car-Parrinello method

Symplectic numerical integration

Software for molecular mechanics modeling

Dynamical systems

Theoretical chemistry

Statistical mechanics

Quantum chemistry

Discrete element method

List of nucleic acid simulation software

Molecular dynamics 130

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9398.

[12] Tersoff, J. (1989). ""Modeling solid-state chemistry: Interatomic potentials for multicomponent systems".

Phys. Rev. B 39: 5566. doi: 10.1103/PhysRevB.39.5566 (http://dx.doi.org/10.1103/PhysRevB.39.5566).
[13] Daw, M. S.; S. M. Foiles and M. I. Baskes (1993). "The embedded-atom method: a review of theory and

applications". Mat. Sci. And Engr. Rep. 9: 251. doi: 10.1016/0920-2307(93)90001-U (http://dx.doi.org/10.

1016/0920-2307(93)90001-U).
[14] Cleri, F.; V. Rosato (1993). "Tight-binding potentials for transition metals and alloys". Phys. Rev. B 48: 22.

doi: 10.1103/PhysRevB.48.22 (http://dx.doi.org/10.1103/PhysRevB.48.22).
[15] Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD (2006). "A polarizable model of water for

molecular dynamics simulations of biomolecules". Chem Phys Lett 418: 245-249. doi:

10.1016/j.cplett.2005.10.135 (http://dx.doi.Org/10.1016/j.cplett.2005.10.135).
[16] Patel, S. ; MacKerell, Jr. AD; Brooks III, Charles L (2004). "CHARMM fluctuating charge force field for

proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic

model". J ComputChem 25: 1504-1514. doi: 10. 1002/jcc. 20077 (http://dx.doi.org/10.1002/jcc.20077).
[17] Billeter, SR; SP Webb, PK Agarwal, T Iordanov, S Hammes-Schiffer (2001). "Hydride Transfer in Liver Alcohol

Dehydrogenase: Quantum Dynamics, Kinetic Isotope Effects, and Role of Enzyme Motion". J Am Chem Soc 123:

11262-11272. doi: 10.1021/ja011384b (http://dx.doi.org/10.1021/ja011384b).
[18] Smith, A; CK Hall (2001). "Alpha-Helix Formation: Discontinuous Molecular Dynamics on an

Intermediate-Resolution Protein Model". Proteins 44: 344-360.
[19] Ding, F; JM Borreguero, SV Buldyrey, HE Stanley, NV Dokholyan (2003). "Mechanism for the alpha-helix to

beta-hairpin transition". J Am Chem Soc 53: 220-228. doi: 10.1002/prot. 10468 (http://dx.doi.org/10.1002/

prot. 10468).
[20] Paci, E; M Vendruscolo, M Karplus (2002). "Validity of Go Models: Comparison with a Solvent-Shielded

Empirical Energy Decomposition". Biophys J 83: 3032-3038. doi: 10.1016/S0006-3495(02)75308-3 (http : //dx.

doi.org/10.1016/S0006-3495(02)75308-3).
[21] McCammon, J; JB Gelin, M Karplus (1977). "Dynamics of folded proteins". Nature 267: 585-590. doi:

10.1038/267585a0 (http://dx.doi.org/10.1038/267585a0).
[22] Averback, R. S.; Diaz de la Rubia, T. (1998). "Displacement damage in irradiated metals and semiconductors".

in H. Ehrenfest and F. Spaepen. Solid State Physics. 51. New York: Academic Press, p. 281-402.
[23] R. Smith, ed (1997). Atomic & ion collisions in solids and at surfaces: theory, simulation and applications.

Cambridge, UK: Cambridge University Press.
[24] Freddolino P, Arkhipov A, Larson SB, McPherson A, Schulten K.

http://www.ks.uiuc.edu/Research/STMV/! "Molecular dynamics simulation of the Satellite Tobacco Mosaic Virus

Molecular dynamics 131

(STMV)". Theoretical and Computational Biophysics Group. University of Illinois at Urbana Champaign, http://

www.ks.uiuc.edu/Research/STMV/.

[25] The Folding@Home Project (http://folding.stanford.edu/) and recent papers (http://folding.stanford.edu/

papers.html) published using trajectories from it. Vijay Pande Group. Stanford University

[26] http://www.cs.sandia.gov/~sjplimp/md.html

[27] http://cbbl.imim.es/Adun

[28] http://www.agilemolecule.com/Products.html

[29] http://cp2k.berlios.de/

[30] http://www.DEShawResearch.com/resources.html

[31] http://www.ccp5.ac.uk/DL_P0LY/

[32] http://fireball-dft.org

[33] http://www.biowerkzeug.com/

[34] http://ccpforge.cse.rl.ac.uk/frs/?group_id=34

[35] http://www.univie.ac.at/newtonx/

[36] http://protomol.sourceforge.net/

[37] http://www.sphinxlib.de

[38] http://www.yasara.org

[39] http://www.chim.unifi.it/orac/

[40] http://esra.sourceforge.net/cgi-bin/index.cgi

[41] http ://mw. concord, org/modeler/

General references

• M. P. Allen, D. J. Tildesley (1989) Computer simulation of liquids. Oxford University
Press. ISBN 0-19-855645-4.

• J. A. McCammon, S. C. Harvey (1987) Dynamics of Proteins and Nucleic Acids.
Cambridge University Press. ISBN 0521307503 (hardback).

• D. C. Rapaport (1996) The Art of Molecular Dynamics Simulation. ISBN 0-521-44561-2.

• Frenkel, Daan; Smit, Berend (2002) [2001]. Understanding Molecular Simulation : from
algorithms to applications. San Diego, California: Academic Press. ISBN 0-12-267351-4.

• J. M. Haile (2001) Molecular Dynamics Simulation: Elementary Methods. ISBN
0-471-18439-X

• R. J. Sadus, Molecular Simulation of Fluids: Theory, Algorithms and Object-Orientation,
2002, ISBN 0-444-51082-6

• Oren M. Becker, Alexander D. Mackerell Jr, Benoit Roux, Masakatsu Watanabe (2001)
Computational Biochemistry and Biophysics. Marcel Dekker. ISBN 0-8247-0455-X.

• Andrew Leach (2001) Molecular Modelling: Principles and Applications. (2nd Edition)
Prentice Hall. ISBN 978-0582382107.

• Tamar Schlick (2002) Molecular Modeling and Simulation. Springer. ISBN
0-387-95404-X.

• William Graham Hoover (1991) Computational Statistical Mechanics, Elsevier, ISBN
0-444-88192-1.

Molecular dynamics 132

External links

• The Blue Gene Project (http://researchweb.watson.ibm.com/bluegene/) (IBM)

• D. E. Shaw Research (http://deshawresearch.com/) (D. E. Shaw Research)

• Molecular Physics (http://www.tandf.co.uk/journals/titles/00268976.asp)

• Statistical mechanics of Nonequilibrium Liquids (http://www.phys.unsw.edu.au/
~gary/book.html) Lecture Notes on non-equilibrium MD

• Introductory Lecture on Classical Molecular Dynamics (http://www.fz-juelich.de/
nic-series/volumelO/sutmann.pdf) by Dr. Godehard Sutmann, NIC, Forschungszentrum
Jiilich, Germany

• Introductory Lecture on Ab Initio Molecular Dynamics and Ab Initio Path Integrals (http:/
/www. fz-juelich.de/nic-series/volumel0/tuckerman2.pdf) by Mark E. Tuckerman,

New York University, USA

• Introductory Lecture on Ab initio molecular dynamics: Theory and Implementation (http:/
/www.fz-juelich.de/nic-series/Volumel/marx.pdf) by Dominik Marx, Ruhr-Universitat
Bochum and Jiirg Hutter, Universitat Zurich

CHARMM 133

CHARMM

Developer(s)

Martin Karplus, Accelrys

Initial release

1983

Stable release

c35b2/ 2008-12-28

Preview release

c36a2 / 2009-02-15

Written in

Ratfor

Operating system

Unix-like

Type

molecular dynamics

License

The CHARMM Development Project

Website

charmm.org

CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a

widely used set of force fields for molecular dynamics as well as the name for the molecular

rn r2i
dynamics simulation and analysis package associated with them. The CHARMM

Development Project involves a network of developers throughout the world working with

Martin Karplus and his group at Harvard to develop and maintain the CHARMM program.

Licenses for this software are available, for a fee, to people and groups working in

academia.

The commercial version of CHARMM, called CHARMm (note the lowercase 'm'), is
available from Accelrys.

CHARMM force fields

The CHARMM force fields for proteins include: united-atom (sometimes called "extended
atom") CHARMM19 [3] , all-atom CHARMM22 [4] and its dihedral potential corrected variant
CHARMM22/CMAP. [5] In the CHARMM22 protein force field, the atomic partial charges
were derived from quantum chemical calculations of the interactions between model
compounds and water. Furthermore, CHARMM22 is parametrized for the TIP3P explicit
water model. Nevertheless, it is frequently used with implicit solvents. Recently, a special
version of CHARMM22/CMAP was reparametrized for consistent use with implicit solvent
GBSW. [6]

For DNA, RNA, and lipids, CHARMM27 [7] is used. Some force fields may be combined, for
example CHARMM22 and CHARMM27 for the simulation of protein-DNA binding.
Additionally, parameters for NAD+, sugars, fluorinated compounds, etc. may be
downloaded [ . These force field version numbers refer to the CHARMM version where
they first appeared, but may of course be used with subsequent versions of the CHARMM
executable program. Likewise, these force fields may be used within other molecular
dynamics programs that support them.

CHARMM also includes polarizable force fields using two approaches. One is based on the
fluctuating charge (FQ) model, also known as Charge Equilibration (CHEQ). [ ] [ ^ The
other is based on the Drude shell or dispersion oscillator model.

CHARMM 134

CHARMM molecular dynamics program

The CHARMM program allows generation and analysis of a wide range of molecular
simulations. The most basic kinds of simulation are minimization of a given structure and
production runs of a molecular dynamics trajectory.

More advanced features include free energy perturbation (FEP), quasi-harmonic entropy
estimation, correlation analysis and combined quantum, and molecular mechanics
(QM/MM) methods.

CHARMM is one of the oldest programs for molecular dynamics. It has accumulated a huge
number of features, some of which are duplicated under several keywords with slight
variations. This is an inevitable result of the large number of outlooks and groups working
on CHARMM throughout the world. The changelog file [13] as well as CHARMM's source
code are good places to look for the names and affiliations of the main developers. The
involvement and coordination by Charles L. Brooks Ill's group at the University of Michigan
is very salient.

History of the program

Around 1969, there was considerable interest in developing potential energy functions for
small molecules. CHARMM originated at Martin Karplus's group at Harvard. Karplus and
his then graduate student Bruce Gelin decided the time was ripe to develop a program that
would make it possible to take a given amino acid sequence and a set of coordinates (e.g.,
from the X-ray structure) and to use this information to calculate the energy of the system
as a function of the atomic positions. Karplus has acknowledged the importance of major
inputs in the development of the (still nameless) program, including

• Schneior Lifson's group at the Weizmann Institute, especially from Arieh Warshel who
went to Harvard and brought his consistent force field (CCF) program with him;

• Harold Scheraga's group at Cornell University; and

• Awareness of Michael Levitt's pioneering energy calculations for proteins

In the 1980s, finally a paper appeared and CHARMM made its public debut. Gelin's
program had by then been considerably restructured. For the publication, Bob Bruccoleri
came up with the name HARMM (HARvard Macromolecular Mechanics), but it didn't seem
appropriate. So they added a C for Chemistry. Karplus said: "I sometimes wonder if
Bruccoleri' s original suggestion would have served as a useful warning to inexperienced
scientists working with the program." CHARMM has continued to grow and the latest
release of the executable program was made in August 2008 as CHARMM35M.

Running CHARMM Under Unix/Linux

The general syntax for using the program is:
charmm < filename. inp > filename. out

charmm

The actual name of the program (or script which runs the program) on the computer
system being used.

filename. inp

CHARMM 135

A text file which contains the CHARMM commands. It starts by loading the molecular
topologies (top) and force field (par). Then one loads the molecular structures'
Cartesian coordinates (e.g. from PDB files). One can then modify the molecules
(adding hydrogens, changing secondary structure). The calculation section can include
energy minimization, dynamics production, and analysis tools such as motion and
energy correlations.
filename. out

The log file for the CHARMM run, containing echoed commands, and various amounts
of command output. The output print level may be increased or decreased in general,
and procedures such as minimization and dynamics have printout frequency
specifications. The values for temperature, energy pressure, etc. are output at that
frequency.

CHARMM and Volunteer Computing

Docking@Home, hosted by University of Delaware, one of the projects which use a
opensource platform for the distributed computing, BOINC, adopts CHARMM to analyze
the atomic details of protein-ligand interactions in terms of Molecular Dynamics (MD)
simulations and minimizations.

World Community Grid, sponsored by IBM, runs a project called The Clean Energy Project
[15] which also uses CHARMM.

See also

• AMBER

• Force field implementation

References

[1] Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983). "CHARMM: A program

for macromolecular energy, minimization, and dynamics calculations". J Comp Chem 4: 187-217. doi:

10.1002/jcc.540040211 (http://dx.doi.org/10.1002/jcc.540040211).
[2] MacKerell, A.D., Jr.; Brooks, B. ; Brooks, C. L., Ill; Nilsson, L. ; Roux, B. ; Won, Y. ; Karplus, M. (1998).

"CHARMM: The Energy Function and Its Parameterization with an Overview of the Program", in Schleyer,

P.v.R.; et al.. The Encyclopedia of Computational Chemistry. 1. Chichester: John Wiley & Sons. pp. 271-277 '.
[3] Reiher, III WH (1985). "Theoretical studies of hydrogen bonding". PhD Thesis at Harvard University.
[4] MacKerell, Jr. AD, et al. (1998). "All-atom empirical potential for molecular modeling and dynamics studies of

proteins".J"P/ii;sC/iemB 102: 3586-3616. doi: 10. 1021/jp973084f (http://dx.doi.org/10.1021/jp973084f).
[5] MacKerell, Jr. AD, Feig M, Brooks, III CL (2004). "Extending the treatment of backbone energetics in protein

force fields: limitations of gas-phase guantum mechanics in reproducing protein conformational distributions in

molecular dynamics simulations". J Comput Chem 25: 1400-1415. doi: 10. 1002/jcc. 20065 (http://dx.doi.org/

10. 1002/jcc. 20065).
[6] Brooks CL, Chen J, Im W (2006). "Balancing solvation and intramolecular interactions: toward a consistent

generalized born force field (CMAP opt. for GBSW)". J Am Chem Soc 128: 3728-3736. doi: 10.1021/ja057216r

(http://dx.doi.org/10.1021/ja057216r).
[7] MacKerell, Jr. AD, Banavali N, Foloppe N (2001). "Development and current status of the CHARMM force field

for nucleic acids". Biopolymers 56: 257-265. doi:

10. 1002/1097-0282(2000)56:4<257::AID-BIP10029>3.0.CO;2-W (http://dx.doi.org/10.1002/

1097-0282(2000)56:4<257:AID-BIP10029>3.0.CO;2-W).
[8] http://mackerell.umaryland.edu/CHARMM_ff_params.html
[9] Patel, S. ; MacKerell, Jr. AD; Brooks III, Charles L (2004). "CHARMM fluctuating charge force field for proteins:

I parameterization and application to bulk organic liguid simulations". J Comput Chem 25: 1-15. doi:

10.1002/jcc.l0355 (http://dx.doi.org/10.1002/jcc.10355).

CHARMM 136

[10] Patel, S. ; MacKerell, Jr. AD; Brooks III, Charles L (2004). "CHARMM fluctuating charge force field for
proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic
model". J ComputChem 25: 1504-1514. doi: 10. 1002/jcc. 20077 (http://dx.doi.org/10.1002/jcc.20077).

[11] Lamoureux G, Roux B. (2003). Modeling induced polarization with classical Drude oscillators: Theory and
molecular dynamics simulation algorithm. J Chem Phys 119(6):3025-3039.

[12] Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD. (2006). A polarizable model of water for
molecular dynamics simulations of biomolecules. Chem Phys Lett 418:245-9.

[13] http ://www. charmm.org/package/changelogs/c341og.shtml

[14] Karplus M (2006). "Spinach on the ceiling: a theoretical chemist's return to biology". Annu Rev Biophys
Biomol Struct 35: 1-47. doi: 10. 1146/annurev.biophys. 33. 110502. 133350 (http://dx.doi.org/10.1146/
annurev.biophys. 33. 110502. 133350).

[15] http ://www. worldcommunitygrid. org/proj ectsshowcase/cep 1/viewCep 1 Main. do

External links

• Accelrys website (http://www.accelrys.com/)

• CHARMM website (http://www.charmm.org/) with documentation (http://www.
charmm.org/html/documentation/chmdoc.html) and helpful discussion forums (http://
165. 1 1 2. 184. 1 3//ubbthreads/ubbthreads.php?Cat=)

• CHARMM tutorial (http://www.ch.embnet.org/MD_tutorial/)

• MacKerell (http://www.pharmacy.umaryland.edu/faculty/amackere/) website
including a Package of force field parameters for CHARMM (http://mackerell.
umaryland.edu/CHARMM_ff_params.html)

• C.Brooks website (http://www.scripps.edu/brooks/)

• CHARMM page at Harvard (http://yuri.harvard.edu/)

• Roux website (http://thallium.bsd.uchicago.edu/RouxLab/index.html)

• Bernard R. Brooks Group Website (http://www.lobos.nih.gov/cbs/index.php)

• VMD (http://www.ks.uiuc.edu/Research/vmd/) - visualization of CHARMM
trajectories

• Sirius (http://sirius.sdsc.edu) - visualization of CHARMM trajectories

• Docking@Home (http://docking.cis.udel.edu/)

Statistical mechanics 137

Statistical mechanics

Statistical mechanics (or statistical thermodynamics ) is the application of
probability theory, which includes mathematical tools for dealing with large populations, to
the field of mechanics, which is concerned with the motion of particles or objects when
subjected to a force. It provides a framework for relating the microscopic properties of
individual atoms and molecules to the macroscopic or bulk properties of materials that can
be observed in everyday life, therefore explaining thermodynamics as a natural result of
statistics and mechanics (classical and quantum) at the microscopic level.

It provides a molecular-level interpretation of thermodynamic quantities such as work,
heat, free energy, and entropy, allowing the thermodynamic properties of bulk materials to
be related to the spectroscopic data of individual molecules. This ability to make
macroscopic predictions based on microscopic properties is the main advantage of
statistical mechanics over classical thermodynamics. Both theories are governed by the
second law of thermodynamics through the medium of entropy. However, entropy in
thermodynamics can only be known empirically, whereas in statistical mechanics, it is a
function of the distribution of the system on its micro-states.

Statistical thermodynamics was born in 1870 with the work of Austrian physicist Ludwig
Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas
Theory} ' Boltzmann's original papers on the statistical interpretation of thermodynamics,
the H-theorem, transport theory, thermal equilibrium, the equation of state of gases, and
similar subjects, occupy about 2,000 pages in the proceedings of the Vienna Academy and
other societies. The term "statistical thermodynamics" was proposed for use by the
American thermodynamicist and physical chemist J. Willard Gibbs in 1902. According to
Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first
used by the Scottish physicist James Clerk Maxwell in 1871.

Overview

The essential problem in statistical thermodynamics is to determine the distribution of a
given amount of energy E over N identical systems. The goal of statistical
thermodynamics is to understand and to interpret the measurable macroscopic properties
of materials in terms of the properties of their constituent particles and the interactions
between them. This is done by connecting thermodynamic functions to quantum-mechanic
equations. Two central quantities in statistical thermodynamics are the Boltzmann factor
and the partition function.

Statistical mechanics 138

Fundamentals

Central topics covered in statistical thermodynamics include:

Microstates and configurations

Boltzmann distribution law

Partition function, Configuration integral or configurational partition function

Thermodynamic equilibrium - thermal, mechanical, and chemical.

Internal degrees of freedom - rotation, vibration, electronic excitation, etc.

Heat capacity - Einstein solids, polyatomic gases, etc.

Nernst heat theorem

Fluctuations

Gibbs paradox

Degeneracy

Lastly, and most importantly, the formal definition of entropy of a thermodynamic system
from a statistical perspective is called statistical entropy, and is defined as:

S = k B lnn
where

k D is Boltzmann's constant 1.38066xl0 -23 J K _1 and

B J

fiis the number of microstates corresponding to the observed thermodynamic

macrostate.
A common mistake is taking this formula as a hard general definition of entropy. This
equation is valid only if each microstate is equally accessible (each microstate has an equal
probability of occurring).

Boltzmann Distribution

If the system is large the Boltzmann distribution could be used (the Boltzmann distribution
is an approximate result)

71; <X e k B T .

n.
This can now be used with Pi

N yiEll levels -i^r

History

In 1738, Swiss physicist and mathematician Daniel Bernoulli published Hydrodynamica
which laid the basis for the kinetic theory of gases. In this work, Bernoulli positioned the
argument, still used to this day, that gases consist of great numbers of molecules moving in
all directions, that their impact on a surface causes the gas pressure that we feel, and that
what we experience as heat is simply the kinetic energy of their motion.

In 1859, after reading a paper on the diffusion of molecules by Rudolf Clausius, Scottish
physicist James Clerk Maxwell formulated the Maxwell distribution of molecular velocities,
which gave the proportion of molecules having a certain velocity in a specific range. This
was the first-ever statistical law in physics. Five years later, in 1864, Ludwig Boltzmann,
a young student in Vienna, came across Maxwell's paper and was so inspired by it that he

Statistical mechanics 139

spent much of his long and distinguished life developing the subject further.

Hence, the foundations of statistical thermodynamics were laid down in the late 1800s by
those such as Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius, and Willard Gibbs
who began to apply statistical and quantum atomic theory to ideal gas bodies.
Predominantly, however, it was Maxwell and Boltzmann, working independently, who
reached similar conclusions as to the statistical nature of gaseous bodies. Yet, one must
consider Boltzmann to be the "father" of statistical thermodynamics with his 1875
derivation of the relationship between entropy S and multiplicity O, the number of
microscopic arrangements (microstates) producing the same macroscopic state
(macrostate) for a particular system. ^

Fundamental postulate

The fundamental postulate in statistical mechanics (also known as the equal a priori
probability postulate) is the following:

Given an isolated system in equilibrium, it is found with equal probability in each of its
accessible microstates.

This postulate is a fundamental assumption in statistical mechanics - it states that a system
in equilibrium does not have any preference for any of its available microstates. Given Q
microstates at a particular energy, the probability of finding the system in a particular
microstate is p = 1/Q.

This postulate is necessary because it allows one to conclude that for a system at
equilibrium, the thermodynamic state (macrostate) which could result from the largest
number of microstates is also the most probable macrostate of the system.

The postulate is justified in part, for classical systems, by Liouville's theorem (Hamiltonian),
which shows that if the distribution of system points through accessible phase space is
uniform at some time, it remains so at later times.

Similar justification for a discrete system is provided by the mechanism of detailed balance.

This allows for the definition of the information function (in the context of information
theory):

J = -"^pilnpi = {Inp}.
i
When all the probabilities (rhos) are equal, I is maximal, and we have minimal information

about the system. When our information is maximal (i.e., one rho is equal to one and the

rest to zero, such that we know what state the system is in), the function is minimal.

This "information function" is the same as the reduced entropic function in

thermodynamics.

Statistical mechanics 140

Statistical ensembles

Microcanonical ensemble

In microcanonical ensemble N, V and E are fixed. Since the second law of thermodynamics
applies to isolated systems, the first case investigated will correspond to this case. The
Microcanonical ensemble describes an isolated system.

The entropy of such a system can only increase, so that the maximum of its entropy
corresponds to an equilibrium state for the system.

Because an isolated system keeps a constant energy, the total energy of the system does
not fluctuate. Thus, the system can access only those of its micro-states that correspond to
a given value E of the energy. The internal energy of the system is then strictly equal to its
energy.

Let us call SX-E)the number of micro-states corresponding to this value of the system's
energy. The macroscopic state of maximal entropy for the system is the one in which all
micro-states are equally likely to occur, with probability l/fi(.E), during the system's
fluctuations.

S =

IUE) ( . .. x

where

S is the system entropy, and

freis Boltzmann's constant.

Canonical ensemble

In canonical ensemble N, V and T are fixed. Invoking the concept of the canonical
ensemble, it is possible to derive the probability ^that a macroscopic system in thermal
equilibrium with its environment, will be in a given microstate with energy E-i according to
the Boltzmann distribution:

Pi =

e -m

where 3 = — ,

The temperature T arises from the fact that the system is in thermal equilibrium with its
environment. The probabilities of the various microstates must add to one, and the
normalization factor in the denominator is the canonical partition function:

J-max

,. :
where Ei is the energy of the i th microstate of the system. The partition function is a
measure of the number of states accessible to the system at a given temperature. The
article canonical ensemble contains a derivation of Boltzmann's factor and the form of the
partition function from first principles.

To sum up, the probability of finding a system at temperature Tin a particular state with
energy £;is

Statistical mechanics 141

Thermodynamic Connection

The partition function can be used to find the expected (average) value of any microscopic
property of the system, which can then be related to macroscopic variables. For instance,
the expected value of the microscopic energy £is interpreted as the microscopic definition
of the thermodynamic variable internal energy U , and can be obtained by taking the
derivative of the partition function with respect to the temperature. Indeed,

(E) gjj^!f: 1^

V ' Z Zdd

implies, together with the interpretation of {E) as U , the following microscopic definition
of internal energy:

The entropy can be calculated by (see Shannon entropy)
S e-P E '

"- ■' ; £*

\ \

which implies that

jm = u _ TS = F

Q
is the free energy of the system or in other words,

Z = e-0*
Having microscopic expressions for the basic thermodynamic potentials U (internal
energy), S (entropy) and F{free energy) is sufficient to derive expressions for other
thermodynamic quantities. The basic strategy is as follows. There may be an intensive or
extensive quantity that enters explicitly in the expression for the microscopic energy Ei ,
for instance magnetic field (intensive) or volume (extensive). Then, the conjugate
thermodynamic variables are derivatives of the internal energy. The macroscopic
magnetization (extensive) is the derivative of [/with respect to the (intensive) magnetic
field, and the pressure (intensive) is the derivative of [/with respect to volume (extensive).
The treatment in this section assumes no exchange of matter (i.e. fixed mass and fixed
particle numbers). However, the volume of the system is variable which means the density
is also variable.

This probability can be used to find the average value, which corresponds to the
macroscopic value, of any property, J , that depends on the energetic state of the system
by using the formula:

e~ pEi

i i

where {J) is the average value of property J . This equation can be applied to the internal
energy, U :

p -pBi

Subsequently, these equations can be combined with known thermodynamic relationships
between U and \ 'to arrive at an expression for pressure in terms of only temperature,
volume and the partition function. Similar relationships in terms of the partition function
can be derived for other thermodynamic properties as shown in the following table; see also

Statistical mechanics

142

the detailed explanation in configuration integral

[6]

Helmholtz free energy:

Internal energy:

Pressure:

(8F\ 1 (d\nZ\
\dv) NT P\8V) NT

Entropy:

3 = k(\n Z + BU)

Gibbs free energy:

° — ~¥ + H^L

Enthalpy:

H = U + PV

Constant volume heat capacity:

*"(SL

Constant pressure heat capacity:

*-(£)„

Chemical potential:

1 (8\nZ\

To clarify, this is not a grand canonical ensemble.

It is often useful to consider the energy of a given molecule to be distributed among a
number of modes. For example, translational energy refers to that portion of energy
associated with the motion of the center of mass of the molecule. Configurational energy
refers to that portion of energy associated with the various attractive and repulsive forces
between molecules in a system. The other modes are all considered to be internal to each
molecule. They include rotational, vibrational, electronic and nuclear modes. If we assume
that each mode is independent (a questionable assumption) the total energy can be
expressed as the sum of each of the components:

hi = hit -\- h/ c -\- hj n -\- ±L e -\- £; r -|- hi v
Where the subscripts t , c t n, e, r t and v correspond to translational, configurational,
nuclear, electronic, rotational and vibrational modes, respectively. The relationship in this
equation can be substituted into the very first equation to give:

- ,3 (£■',,+£„+£„, +£ =; +£V; +£„; )

e -/3£',; e -.s£'c, e -£ £ ™ e ~ pE=i e~ pB " e - * 3 ^

If we can assume all these modes are completely uncoupled and uncorrelated, so all these
factors are in a probability sense completely independent, then

Thus a partition function can be defined for each mode. Simple expressions have been
derived relating each of the various modes to various measurable molecular properties,
such as the characteristic rotational or vibrational frequencies.

Expressions for the various molecular partition functions are shown in the following table.

Nuclear

(T < 10 s K)

Statistical mechanics

143

Electronic

Z e = Woe ^n a+ w^o^ + ...

Vibrational

e -fl.j/2T

Z * " II 1 _ -i^/r

Rotational (linear)

Rotational (non-linear)

1 / ttT 3

Translational

[2-KmkTf^

Configurational (ideal gas)

Z, = V

These equations can be combined with those in the first table to determine the contribution
of a particular energy mode to a thermodynamic property. For example the "rotational
pressure" could be determined in this manner. The total pressure could be found by
summing the pressure contributions from all of the individual modes, ie:

P = P t + P c + P n + P e + Pt + P.

Grand canonical ensemble

In grand canonical ensemble V, Tand chemical potential are fixed. If the system under
study is an open system, (matter can be exchanged), but particle number is not conserved,
we would have to introduce chemical potentials, u., j = l,...,n and replace the canonical
partition function with the grand canonical partition function:

H(V,2»=X> X P [p

where N.. is the number of i

•th

species particles in the i configuration. Sometimes, we also
have other variables to add to the partition function, one corresponding to each conserved
quantity. Most of them, however, can be safely interpreted as chemical potentials. In most
condensed matter systems, things are nonrelativistic and mass is conserved. However, most
condensed matter systems of interest also conserve particle number approximately
(metastably) and the mass (nonrelativistically) is none other than the sum of the number of
each type of particle times its mass. Mass is inversely related to density, which is the
conjugate variable to pressure. For the rest of this article, we will ignore this complication
and pretend chemical potentials don't matter. See grand canonical ensemble.

Let's rework everything using a grand canonical ensemble this time. The volume is left
fixed and does not figure in at all in this treatment. As before, j is the index for those
particles of species j and i is the index for microstate z:

Bxpi-PiEt-EjfyXv))

exp(-/?(E i -£ j Mj%))

Grand potential:

<I>,

In 5
'IT

Internal energy:

/9]ns\ „ fij / 91na \

Statistical mechanics 144

Particle number:

Al /3 V 9fM ),

Entropy:

S = k(\nE + SU -8^2 fiiNi)

Helmholtz free energy:

lnE ^^ lit /91n5\

Equivalence between descriptions at the thermodynamic limit

All of the above descriptions differ in the way they allow the given system to fluctuate
between its configurations.

In the micro-canonical ensemble, the system exchanges no energy with the outside world,
and is therefore not subject to energy fluctuations; in the canonical ensemble, the system is
free to exchange energy with the outside in the form of heat.

In the thermodynamic limit, which is the limit of large systems, fluctuations become
negligible, so that all these descriptions converge to the same description. In other words,
the macroscopic behavior of a system does not depend on the particular ensemble used for
its description.

Given these considerations, the best ensemble to choose for the calculation of the
properties of a macroscopic system is that ensemble which allows the result to be derived
most easily.

Random walks

The study of long chain polymers has been a source of problems within the realms of
statistical mechanics since about the 1950s. One of the reasons however that scientists
were interested in their study is that the equations governing the behaviour of a polymer
chain were independent of the chain chemistry. What is more, the governing equation turns
out to be a random (diffusive) walk in space. Indeed, the Schrodinger equation is itself a
diffusion equation in imaginary time, t' = it .

Random walks in time

The first example of a random walk is one in space, whereby a particle undergoes a random
motion due to external forces in its surrounding medium. A typical example would be a
pollen grain in a beaker of water. If one could somehow "dye" the path the pollen grain has
taken, the path observed is defined as a random walk.

Consider a toy problem, of a train moving along a ID track in the x-direction. Suppose that
the train moves either a distance of + or - a fixed distance b, depending on whether a coin
lands heads or tails when flipped. Lets start by considering the statistics of the steps the toy
train takes (where Sjis the ith step taken):

(Si) = 0; due to a priori equal probabilities
{SiS 3 } = &%.

The second quantity is known as the correlation function. The delta is the kronecker delta
which tells us that if the indices i and j are different, then the result is 0, but if i = j then the
kronecker delta is 1, so the correlation function returns a value of b 2 - This makes sense,
because if z = j then we are considering the same step. Rather trivially then it can be shown

Statistical mechanics 145

that the average displacement of the train on the x-axis is 0;

1=1

z=l

X=l

As stated {Si} is 0, so the sum of is still 0. It can also be shown, using the same method
demonstrated above, to calculate the root mean square value of problem. The result of this
calculation is given below

■"rras y \ / DVjIi.

From the diffusion equation it can be shown that the distance a diffusing particle moves in
a media is proportional to the root of the time the system has been diffusing for, where the
proportionality constant is the root of the diffusion constant. The above relation, although
cosmetically different reveals similar physics, where N is simply the number of steps moved
(is loosely connected with time) and b is the characteristic step length. As a consequence
we can consider diffusion as a random walk process.

Random walks in space

Random walks in space can be thought of as snapshots of the path taken by a random
walker in time. One such example is the spatial configuration of long chain polymers.

There are two types of random walk in space: self-avoiding random walks, where the links
of the polymer chain interact and do not overlap in space, and pure random walks, where
the links of the polymer chain are non-interacting and links are free to lie on top of one
another. The former type is most applicable to physical systems, but their solutions are
harder to get at from first principles.

By considering a freely jointed, non-interacting polymer chain, the end-to-end vector is

R = ^T; where r tis the vector position of the z'-th link in the chain. As a result of the

i=i
central limit theorem, if N >> 1 then we expect a Gaussian distribution for the end-to-end
vector. We can also make statements of the statistics of the links themselves;
{i\} = 0; by the isotropy of space

{rj ■ Tj) = 3£r<5jj; all the links in the chain are uncorrelated with one another
Using the statistics of the individual links, it is easily shown that {R} = Oand
(R ■ R) = 3Nb . Notice this last result is the same as that found for random walks in time.

Assuming, as stated, that that distribution of end-to-end vectors for a very large number of
identical polymer chains is gaussian, the probability distribution has the following form

1 -3R R

p^Y /g eXP 2JV6 2

What use is this to us? Recall that according to the principle of equally likely a priori
probabilities, the number of microstates, CI, at some physical value is directly proportional
to the probability distribution at that physical value, viz;

Q (R) = cP (R)

Statistical mechanics 146

where c is an arbitrary proportionality constant. Given our distribution function, there is a

maxima corresponding to R = . Physically this amounts to there being more microstates

which have an end-to-end vector of than any other microstate. Now by considering

S(R)=fe fl lnfi(R)

AS (R) = S (R) - S (0)

AF = -TAS (R)

where F is the Helmholtz free energy it is trivial to show that

A Hookian spring!

This result is known as the Entropic Spring Result and amounts to saying that upon
stretching a polymer chain you are doing work on the system to drag it away from its
(preferred) equilibrium state. An example of this is a common elastic band, composed of
long chain (rubber) polymers. By stretching the elastic band you are doing work on the
system and the band behaves like a conventional spring. What is particularly astonishing
about this result however, is that the work done in stretching the polymer chain can be
related entirely to the change in entropy of the system as a result of the stretching.

Classical thermodynamics vs. statistical thermodynamics

As an example, from a classical thermodynamics point of view one might ask what is it
about a thermodynamic system of gas molecules, such as ammonia NH , that determines
the free energy characteristic of that compound? Classical thermodynamics does not
provide the answer. If, for example, we were given spectroscopic data, of this body of gas
molecules, such as bond length, bond angle, bond rotation, and flexibility of the bonds in
NH we should see that the free energy could not be other than it is. To prove this true, we
need to bridge the gap between the microscopic realm of atoms and molecules and the
macroscopic realm of classical thermodynamics. From physics, statistical mechanics
provides such a bridge by teaching us how to conceive of a thermodynamic system as an
assembly of units. More specifically, it demonstrates how the thermodynamic parameters of
a system, such as temperature and pressure, are interpretable in terms of the parameters

T71

descriptive of such constituent atoms and molecules.

In a bounded system, the crucial characteristic of these microscopic units is that their
energies are quantized. That is, where the energies accessible to a macroscopic system
form a virtual continuum of possibilities, the energies open to any of its submicroscopic
components are limited to a discontinuous set of alternatives associated with integral
values of some quantum number.

Statistical mechanics

147

See also

Chemical thermodynamics

Configuration entropy

Dangerously irrelevant

Paul Ehrenfest

Equilibrium thermodynamics

Fluctuation dissipation theorem

Important Publications in Statistical Mechanics

Ising Model

Mean field theory

Nanomechanics

Non-equilibrium thermodynamics

Quantum thermodynamics

Statistical physics

Thermochemistry

Widom insertion method

Monte Carlo method

Molecular modelling

A Table of Statistical Mechanics Articles

Maxwell Boltzmann

Bose-Einstein

Fermi-Dirac

Particle

Boson

Fermion

Statistics

Partition function
statistical properties

Microcanonical ensemble | Canonical ensemble | Grand canonical ensemble

Statistics

Maxwell-Boltzmann statistics

Maxwell-Boltzmann distribution

Boltzmann distribution

Gibbs paradox

Bose-Einstein statistics

Fermi-Dirac statistics

Thomas-Fermi

gas in a box

approximation

as in a harmonic trap

Gas

Ideal gas

Bose gas

Fermi gas

Debye model

Fermion condensate

Bose-Einstein condensate

Planck's law of black body

radiation

Chemical

Classical Chemical equilibrium

Equilibrium

Statistical mechanics 148

Notes

[1] The terms "Statistical mechanics" and "statistical thermodynamics" are used interchangeably. "Statistical

physics" is a broader term which includes statistical mechanics, but is sometimes also used as a synonym for

statistical mechanics
[2] On history of fundamentals of statistical thermodynamics (http://www.worldscibooks.com/phy_etextbook/

2012/2012_chap01.pdf) (section 1.2)
[3] Schrodinger, Erwin (1946). Statistical Thermodynamics. Dover Publications, Inc.. ISBN 0-486-66101-6. OCLC

20056858 (http://worldcat.org/oclc/20056858).
[4] Mahon, Basil (2003). The Man Who Changed Everything - the Life of James Clerk Maxwell. Hoboken, NJ:

Wiley. ISBN 0-470-86171-1. OCLC 52358254 62045217 (http://worldcat.org/oclc/52358254+62045217).
[5] Perrot, Pierre (1998). AtoZ of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6. OCLC

123283342 38073404 (http://worldcat.org/oclc/123283342 + 38073404).
[6] http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_%28statistical_mechanics%29
[7] Nash, Leonard K. (1974). Elements of Statistical Thermodynamics, 2nd Ed.. Dover Publications, Inc.. ISBN

0-486-44978-5. OCLC 61513215 (http://worldcat.org/oclc/61513215).

References

• Chandler, David (1987). Introduction to Modern Statistical Mechanics. Oxford University
Press. ISBN 0-19-504277-8. OCLC 13946448 (http://worldcat.org/oclc/13946448).

• Huang, Kerson (1990). Statistical Mechanics. Wiley, John & Sons. ISBN 0-471-81518-7.
OCLC 15017884 (http://worldcat.org/oclc/15017884).

• Kittel, Charles; Herbert Kroemer (1980). Thermal Physics (2nd ed.). San Francisco: W.H.
Freeman. ISBN 0716710889. OCLC 5171399 (http://worldcat.org/oclc/5171399).

• McQuarrie, Donald (2000). Statistical Mechanics (2nd rev. Ed.). University Science
Books. ISBN 1-891389-15-7. OCLC 43370175 (http://worldcat.org/oclc/43370175).

• Dill, Ken; Bromberg, Sarina (2003). Molecular Driving Forces. Garland Science. ISBN
0-8153-2051-5. OCLC 47915710 (http://worldcat.org/oclc/47915710).

• List of notable textbooks in statistical mechanics

Further reading

• Ben-Nairn, Arieh (2007). Statistical Thermodynamics Based on Information. ISBN
978-981-270-707-9

• Boltzmann, Ludwig; and Dieter Flamm (2000). Entropie und Wahrscheinlichkeit. ISBN
978-3817132867

• Boltzmann, Ludwig (1896, 1898). [Lectures on gas theory]. New York: Dover. ISBN
0486684555. OCLC 31434905 (http://worldcat.org/oclc/31434905). translated by
Stephen G. Brush (1964) Berkeley: University of California Press; (1995) New York:
Dover ISBN 0-486-68455-5

• Gibbs, J. Willard (1981) [1902]. Elementary principles in statistical dynamics.
Woodbridge, Connecticut: Ox Bow Press. ISBN 0-918024-20-X.

• Landau, Lev Davidovich; and Lifshitz, Evgeny Mikhailovich (1980) [1976]. Statistical
Physics. 5 (3 ed.). Oxford: Pergamon Press. ISBN 0-7506-3372-7. Translated by J.B. Sykes
and M.J. Kearsley

• Reichl, Linda E (1998) [1980]. A modern course in statistical physics (2 ed.). Chichester:
Wiley. ISBN 0-471-59520-9.

Statistical mechanics 149

External links

• Philosophy of Statistical Mechanics (http://plato.stanford.edu/entries/
statphys-statmech/) article by Lawrence Sklar for the Stanford Encyclopedia of
Philosophy.

• Sklogwiki - Thermodynamics, statistical mechanics, and the computer simulation of
materials, (http://www.sklogwiki.org/) SklogWiki is particularly orientated towards
liquids and soft condensed matter.

• Statistical Thermodynamics (http://history.hyperjeff.net/statmech.html) - Historical
Timeline

Statistical field theory

A statistical field theory is any model in statistical mechanics where the degrees of
freedom comprise a field or fields. In other words, the microstates of the system are
expressed through field configurations. It is closely related to quantum field theory, which
describes the quantum mechanics of fields, and shares with it many phenomena, such as
renormalization. If the system involves polymers, it is also known as polymer field theory.

In fact, by performing a Wick rotation from Minkowski space to Euclidean space, many
results of statistical field theory can be applied directly to its quantum equivalent. The
correlation functions of a statistical field theory are called Schwinger functions, and their
properties are described by the Osterwalder-Schrader axioms.

Statistical field theories are widely used to describe systems in polymer physics or
biophysics, such as polymer films, nanostructured block copolymers or polyelectrolytes

References

• Statistical Field Theory volumes I and II (Cambridge Monographs on Mathematical
Physics) by Claude Itzykson, Jean-Michel Drouffe, Publisher: Cambridge University Press;
(March 29, 1991) ISBN 0-521-40806-7 ISBN 0-521-40805-9

• The P(cp) Euclidean (quantum) field theory, by Barry Simon. Princeton Univ Press (June
1974) ISBN 0-691-08144-1

• Quantum Physics: A Functional Integral Point of View by James Glimm, Jaffe. Springer;
2nd edition (May 1987) ISBN 0-387-96477-0

[1] Baeurle SA, Usami T, Gusev AA (2006). "A new multiscale modeling approach for the prediction of mechanical

properties of polymer-based nanomaterials". Polymer 47 : 8604-8617. doi: 10.1016/j.polymer.2006.10.017

(http://dx.doi.Org/10.1016/j.polymer.2006.10.017).
[2] Baeurle SA, Nogovitsin EA (2007). "Challenging scaling laws of flexible polyelectrolyte solutions with effective

renormalization concepts". Polymer 48: 4883-4899. doi: 10.1016/j.polymer.2007.05.080 (http://dx.doi.org/

10.1016/j.polymer.2007.05.080).

Statistical field theory 150

External links

• Problems in Statistical Field Theory (http://www.gursey.gov.tr/~mgh/rg2006/
problemsets.html)

• Particle and Polymer Field Theory Group (http://www-dick.chemie.uni-regensburg.de/
group/stephanbaeurle/)

Computational chemistry

Computational chemistry is a branch of chemistry that uses computers to assist in
solving chemical problems. It uses the results of theoretical chemistry, incorporated into
efficient computer programs, to calculate the structures and properties of molecules and
solids. While its results normally complement the information obtained by chemical
experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is
widely used in the design of new drugs and materials.

Examples of such properties are structure (i.e. the expected positions of the constituent
atoms), absolute and relative (interaction) energies, electronic charge distributions, dipoles
and higher multipole moments, vibrational frequencies, reactivity or other spectroscopic
quantities, and cross sections for collision with other particles.

The methods employed cover both static and dynamic situations. In all cases the computer
time and other resources (such as memory and disk space) increase rapidly with the size of
the system being studied. That system can be a single molecule, a group of molecules, or a
solid. Computational chemistry methods range from highly accurate to very approximate;
highly accurate methods are typically feasible only for small systems. Ab initio methods are
based entirely on theory from first principles. Other (typically less accurate) methods are
called empirical or semi-empirical because they employ experimental results, often from
acceptable models of atoms or related molecules, to approximate some elements of the
underlying theory.

Both ab initio and semi-empirical approaches involve approximations. These range from
simplified forms of the first-principles equations that are easier or faster to solve, to
approximations limiting the size of the system (for example, Periodic boundary conditions),
to fundamental approximations to the underlying equations that are required to achieve any
solution to them at all. For example, most ab initio calculations make the
Born-Oppenheimer approximation, which greatly simplifies the underlying Schrodinger
Equation by freezing the nuclei in place during the calculation. In principle, ab initio
methods eventually converge to the exact solution of the underlying equations as the
number of approximations is reduced. In practice, however, it is impossible to eliminate all
approximations, and residual error inevitably remains. The goal of computational chemistry
is to minimize this residual error while keeping the calculations tractable.

History

Building on the founding discoveries and theories in the history of quantum mechanics, the
first theoretical calculations in chemistry were those of Walter Heitler and Fritz London in
1927. The books that were influential in the early development of computational quantum
chemistry include: Linus Pauling and E. Bright Wilson's 1935 Introduction to Quantum
Mechanics - with Applications to Chemistry, Eyring, Walter and Kimball's 1944 Quantum

Computational chemistry 151

Chemistry, Heitler's 1945 Elementary Wave Mechanics - with Applications to Quantum
Chemistry, and later Coulson's 1952 textbook Valence, each of which served as primary
references for chemists in the decades to follow.

With the development of efficient computer technology in the 1940s, the solutions of
elaborate wave equations for complex atomic systems began to be a realizable objective. In
the early 1950s, the first semi-empirical atomic orbital calculations were carried out.
Theoretical chemists became extensive users of the early digital computers. A very detailed
account of such use in the United Kingdom is given by Smith and Sutcliffe. The first ab
initio Hartree-Fock calculations on diatomic molecules were carried out in 1956 at MIT,
using a basis set of Slater orbitals. For diatomic molecules, a systematic study using a
minimum basis set and the first calculation with a larger basis set were published by Ransil
and Nesbet respectively in 1960. The first polyatomic calculations using Gaussian orbitals
were carried out in the late 1950s. The first configuration interaction calculations were
carried out in Cambridge on the EDSAC computer in the 1950s using Gaussian orbitals by
Boys and coworkers. By 1971, when a bibliography of ab initio calculations was
published, the largest molecules included were naphthalene and azulene. Abstracts

T71

of many earlier developments in ab initio theory have been published by Schaefer.

In 1964, Hiickel method calculations (using a simple linear combination of atomic orbitals
(LCAO) method for the determination of electron energies of molecular orbitals of n
electrons in conjugated hydrocarbon systems) of molecules ranging in complexity from
butadiene and benzene to ovalene, were generated on computers at Berkeley and Oxford.
These empirical methods were replaced in the 1960s by semi-empirical methods such as
CNDO. [9]

In the early 1970s, efficient ab initio computer programs such as ATMOL, GAUSSIAN,
IBMOL, and POLYAYTOM, began to be used to speed up ab initio calculations of molecular
orbitals. Of these four programs, only GAUSSIAN, now massively expanded, is still in use,
but many other programs are now in use. At the same time, the methods of molecular
mechanics, such as MM2, were developed, primarily by Norman Allinger. ]

One of the first mentions of the term "computational chemistry" can be found in the 1970
book Computers and Their Role in the Physical Sciences by Sidney Fernbach and Abraham
Haskell Taub, where they state "It seems, therefore, that 'computational chemistry' can

finally be more and more of a reality." During the 1970s, widely different methods began

n 21
to be seen as part of a new emerging discipline of computational chemistry. 1 J The Journal

of Computational Chemistry was first published in 1980.

Concepts

The term theoretical chemistry may be defined as a mathematical description of chemistry,
whereas computational chemistry is usually used when a mathematical method is
sufficiently well developed that it can be automated for implementation on a computer.
Note that the words exact and perfect do not appear here, as very few aspects of chemistry
can be computed exactly. However, almost every aspect of chemistry can be described in a
qualitative or approximate quantitative computational scheme.

Molecules consist of nuclei and electrons, so the methods of quantum mechanics apply.
Computational chemists often attempt to solve the non-relativistic Schrodinger equation,
with relativistic corrections added, although some progress has been made in solving the
fully relativistic Dirac equation. In principle, it is possible to solve the Schrodinger equation

Computational chemistry 152

in either its time-dependent or time-independent form, as appropriate for the problem in
hand; in practice, this is not possible except for very small systems. Therefore, a great
number of approximate methods strive to achieve the best trade-off between accuracy and
computational cost. Accuracy can always be improved with greater computational cost.
Significant errors can present themselves in ab initio models comprising many electrons,
due to the computational expense of full relativistic-inclusive methods. This complicates the
study of molecules interacting with high atomic mass unit atoms, such as transitional
metals and their catalytic properties. Present algorithms in computational chemistry can
routinely calculate the properties of molecules that contain up to about 40 electrons with
sufficient accuracy. Errors for energies can be less than a few kj/mol. For geometries, bond
lengths can be predicted within a few picometres and bond angles within 0.5 degrees. The
treatment of larger molecules that contain a few dozen electrons is computationally
tractable by approximate methods such as density functional theory (DFT). There is some
dispute within the field whether or not the latter methods are sufficient to describe complex
chemical reactions, such as those in biochemistry. Large molecules can be studied by
semi-empirical approximate methods. Even larger molecules are treated by classical
mechanics methods that employ what are called molecular mechanics. In QM/MM methods,
small portions of large complexes are treated quantum mechanically (QM), and the
remainder is treated approximately (MM).

In theoretical chemistry, chemists, physicists and mathematicians develop algorithms and
computer programs to predict atomic and molecular properties and reaction paths for
chemical reactions. Computational chemists, in contrast, may simply apply existing
computer programs and methodologies to specific chemical questions. There are two
different aspects to computational chemistry:

• Computational studies can be carried out in order to find a starting point for a laboratory
synthesis, or to assist in understanding experimental data, such as the position and
source of spectroscopic peaks.

• Computational studies can be used to predict the possibility of so far entirely unknown
molecules or to explore reaction mechanisms that are not readily studied by experimental
means.

Thus, computational chemistry can assist the experimental chemist or it can challenge the
experimental chemist to find entirely new chemical objects.

Several major areas may be distinguished within computational chemistry:

• The prediction of the molecular structure of molecules by the use of the simulation of
forces, or more accurate quantum chemical methods, to find stationary points on the
energy surface as the position of the nuclei is varied.

• Storing and searching for data on chemical entities (see chemical databases).

• Identifying correlations between chemical structures and properties (see QSPR and
QSAR).

• Computational approaches to help in the efficient synthesis of compounds.

• Computational approaches to design molecules that interact in specific ways with other
molecules (e.g. drug design and catalysis).

Computational chemistry 153

Methods

A single molecular formula can represent a number of molecular isomers. Each isomer is a
local minimum on the energy surface (called the potential energy surface) created from the
total energy (i.e., the electronic energy, plus the repulsion energy between the nuclei) as a
function of the coordinates of all the nuclei. A stationary point is a geometry such that the
derivative of the energy with respect to all displacements of the nuclei is zero. A local
(energy) minimum is a stationary point where all such displacements lead to an increase in
energy. The local minimum that is lowest is called the global minimum and corresponds to
the most stable isomer. If there is one particular coordinate change that leads to a decrease
in the total energy in both directions, the stationary point is a transition structure and the
coordinate is the reaction coordinate. This process of determining stationary points is
called geometry optimization.

The determination of molecular structure by geometry optimization became routine only
after efficient methods for calculating the first derivatives of the energy with respect to all
atomic coordinates became available. Evaluation of the related second derivatives allows
the prediction of vibrational frequencies if harmonic motion is estimated. More importantly,
it allows for the characterization of stationary points. The frequencies are related to the
eigenvalues of the Hessian matrix, which contains second derivatives. If the eigenvalues are
all positive, then the frequencies are all real and the stationary point is a local minimum. If
one eigenvalue is negative (i.e., an imaginary frequency), then the stationary point is a
transition structure. If more than one eigenvalue is negative, then the stationary point is a
more complex one, and is usually of little interest. When one of these is found, it is
necessary to move the search away from it if the experimenter is looking solely for local
minima and transition structures.

The total energy is determined by approximate solutions of the time-dependent Schrodinger
equation, usually with no relativistic terms included, and by making use of the
Born-Oppenheimer approximation, which allows for the separation of electronic and
nuclear motions, thereby simplifying the Schrodinger equation. This leads to the evaluation
of the total energy as a sum of the electronic energy at fixed nuclei positions and the
repulsion energy of the nuclei. A notable exception are certain approaches called direct
quantum chemistry, which treat electrons and nuclei on a common footing. Density
functional methods and semi-empirical methods are variants on the major theme. For very
large systems, the relative total energies can be compared using molecular mechanics. The
ways of determining the total energy to predict molecular structures are:

Ab initio methods

The programs used in computational chemistry are based on many different
quantum-chemical methods that solve the molecular Schrodinger equation associated with
the molecular Hamiltonian. Methods that do not include any empirical or semi-empirical
parameters in their equations - being derived directly from theoretical principles, with no
inclusion of experimental data - are called ab initio methods. This does not imply that the
solution is an exact one; they are all approximate quantum mechanical calculations. It
means that a particular approximation is rigorously defined on first principles (quantum
theory) and then solved within an error margin that is qualitatively known beforehand. If
numerical iterative methods have to be employed, the aim is to iterate until full machine
accuracy is obtained (the best that is possible with a finite word length on the computer,

Computational chemistry

154

electron

correlation
energy

Hartree-Fock energy

Hartree-Fock limit
Post-Hartree-Fock methods

Exact solution of nonrelativistic
Schrodinger equation

— Relativistic energy

Diagram illustrating various ab initio electronic structure
methods in terms of energy. Spacings are not to scale.

and within the mathematical and/or physical approximations made).

The simplest type of ab initio

electronic structure calculation is

the Hartree-Fock (HF) scheme, an

extension of molecular orbital

theory, in which the correlated

electron-electron repulsion is not

specifically taken into account;

only its average effect is included

in the calculation. As the basis set

size is increased, the energy and

wave function tend towards a limit

called the Hartree-Fock limit.

Many types of calculations (known

as post-Hartree-Fock methods)

begin with a Hartree-Fock calculation and subsequently correct for electron-electron

repulsion, referred to also as electronic correlation. As these methods are pushed to the

limit, they approach the exact solution of the non-relativistic Schrodinger equation. In order

to obtain exact agreement with experiment, it is necessary to include relativistic and spin

orbit terms, both of which are only really important for heavy atoms. In all of these

approaches, in addition to the choice of method, it is necessary to choose a basis set. This is

a set of functions, usually centered on the different atoms in the molecule, which are used

to expand the molecular orbitals with the LCAO ansatz. Ab initio methods need to define a

level of theory (the method) and a basis set.

The Hartree-Fock wave function is a single configuration or determinant. In some cases,
particularly for bond breaking processes, this is quite inadequate, and several
configurations need to be used. Here, the coefficients of the configurations and the
coefficients of the basis functions are optimized together.

The total molecular energy can be evaluated as a function of the molecular geometry; in
other words, the potential energy surface. Such a surface can be used for reaction
dynamics. The stationary points of the surface lead to predictions of different isomers and
the transition structures for conversion between isomers, but these can be determined
without a full knowledge of the complete surface.

A particularly important objective, called computational thermochemistry, is to calculate
thermochemical quantities such as the enthalpy of formation to chemical accuracy.
Chemical accuracy is the accuracy required to make realistic chemical predictions and is
generally considered to be 1 kcal/mol or 4 kj/mol. To reach that accuracy in an economic
way it is necessary to use a series of post-Hartree-Fock methods and combine the results.
These methods are called quantum chemistry composite methods.

Computational chemistry 155

Density Functional methods

Density functional theory (DFT) methods are often considered to be ab initio methods for
determining the molecular electronic structure, even though many of the most common
functionals use parameters derived from empirical data, or from more complex calculations.
In DFT, the total energy is expressed in terms of the total one-electron density rather than
the wave function. In this type of calculation, there is an approximate Hamiltonian and an
approximate expression for the total electron density. DFT methods can be very accurate
for little computational cost. Some methods combine the density functional exchange
functional with the Hartree-Fock exchange term and are known as hybrid functional
methods.

Semi-empirical and empirical methods

Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but
make many approximations and obtain some parameters from empirical data. They are very
important in computational chemistry for treating large molecules where the full
Hartree-Fock method without the approximations is too expensive. The use of empirical
parameters appears to allow some inclusion of correlation effects into the methods.

Semi-empirical methods follow what are often called empirical methods, where the
two-electron part of the Hamiltonian is not explicitly included. For n-electron systems, this
was the Hiickel method proposed by Erich Hiickel, and for all valence electron systems, the
Extended Hiickel method proposed by Roald Hoffmann.

Molecular mechanics

In many cases, large molecular systems can be modeled successfully while avoiding
quantum mechanical calculations entirely. Molecular mechanics simulations, for example,
use a single classical expression for the energy of a compound, for instance the harmonic
oscillator. All constants appearing in the equations must be obtained beforehand from
experimental data or ab initio calculations.

The database of compounds used for parameterization, i.e., the resulting set of parameters
and functions is called the force field, is crucial to the success of molecular mechanics
calculations. A force field parameterized against a specific class of molecules, for instance
proteins, would be expected to only have any relevance when describing other molecules of
the same class.

These methods can be applied to proteins and other large biological molecules, and allow
studies of the approach and interaction (docking) of potential drug molecules (eg. [13] and

[14]).

Methods for solids

Computational chemical methods can be applied to solid state physics problems. The
electronic structure of a crystal is in general described by a band structure, which defines
the energies of electron orbitals for each point in the Brillouin zone. Ab initio and
semi-empirical calculations yield orbital energies; therefore, they can be applied to band
structure calculations. Since it is time-consuming to calculate the energy for a molecule, it
is even more time-consuming to calculate them for the entire list of points in the Brillouin
zone.

Computational chemistry 156

Chemical dynamics

Once the electronic and nuclear variables are separated (within the Born-Oppenheimer
representation), in the time-dependent approach, the wave packet corresponding to the
nuclear degrees of freedom is propagated via the time evolution operator (physics)
associated to the time-dependent Schrodinger equation (for the full molecular
Hamiltonian). In the complementary energy-dependent approach, the time-independent
Schrodinger equation is solved using the scattering theory formalism. The potential
representing the interatomic interaction is given by the potential energy surfaces. In
general, the potential energy surfaces are coupled via the vibronic coupling terms.

The most popular methods for propagating the wave packet associated to the molecular
geometry are

• the split operator technique,

• the Multi-Configuration Time-Dependent Hartree method (MCTDH),

• the semiclassical method.

Molecular dynamics (MD) examines (using Newton's laws of motion) the time-dependent
behavior of systems, including vibrations or Brownian motion, using a classical mechanical
description. MD combined with density functional theory leads to the Car-Parrinello
method.

Interpreting molecular wave functions

The Atoms in Molecules model developed by Richard Bader was developed in order to
effectively link the quantum mechanical picture of a molecule, as an electronic
wavefunction, to chemically useful older models such as the theory of Lewis pairs and the
valence bond model. Bader has demonstrated that these empirically useful models are
connected with the topology of the quantum charge density. This method improves on the
use of Mulliken population analysis.

Software packages

There are many self-sufficient software packages used by computational chemists. Some
include many methods covering a wide range, while others concentrating on a very specific
range or even a single method. Details of most of them can be found in:

• Quantum chemistry and solid state physics software supporting several methods.

• Molecular mechanics programs.

• Semi-empirical programs.

• Valence Bond programs.

• Biomolecular modelling programs: proteins, nucleic acid.

Computational chemistry 157

See also

Mathematical chemistry

Molecular modeling

Molecular graphics

Monte Carlo molecular modeling

Quantum chemistry

Basis set (chemistry)

Molecular dynamics

Bioinformatics

Cheminformatics

Computational Chemistry List

Important publications in computational chemistry

International Academy of Quantum Molecular Science

Computational Science

Statistical mechanics

Molecule

Force field in Chemistry

Force field implementation

Cited References

[I] Smith, S. J.; Sutcliffe B. T., (1997). "The development of Computational Chemistry in the United Kingdom".
Reviews in Computational Chemistry 70: 271-316.

[2] Schaefer, Henry F. Ill (1972). The electronic structure of atoms and molecules. Reading, Massachusetss:

Addison-Wesley Publishing Co.. pp. 146.
[3] Boys, S. F.; Cook G. B., Reeves C. M., Shavitt, I. (1956). "Automatic fundamental calculations of molecular

structure". Nature 178 (2): 1207. doi: 10.1038/1781207a0 (http://dx.doi.org/10.1038/1781207a0).
[4] Richards, W. G.; Walker T. E. H and Hinkley R. K. (1971). A bibliography of ab initio molecular wave functions.

Oxford: Clarendon Press.
[5] Preuss, H. (1968). International Journal of Quantum Chemistry 2: 651.
[6] Buenker, R. J. ; Peyerimhoff S. D. (1969). Chemical Physics Letters 3: 37.
[7] Schaefer, Henry F. Ill (1984). Quantum Chemistry. Oxford: Clarendon Press.
[8] Streitwieser, A.; Brauman J. I. and Coulson C. A. (1965). Supplementary Tables of Molecular Orbital

Calculations. Oxford: Pergamon Press.
[9] Pople, John A.; David L. Beveridge (1970). Approximate Molecular Orbital Theory. New York: McGraw Hill.
[10] Allinger, Norman (1977). "Conformational analysis. 130. MM2. A hydrocarbon force field utilizing VI and V2

torsional terms". Journal of the American Chemical Society 99: 8127-8134. doi: 10.1021/ja00467a001 (http://

dx.doi.org/10.1021/ja00467a001).

[II] Fernbach, Sidney; Taub, Abraham Haskell (1970). Computers and Their Role in the Physical Sciences.
Routledge. ISBN 0677140304.

[12] Reviews in Computational Chemistry vol 1, preface (http://www3.interscience.wiley.com/cgi-bin/

bookhome/1 14034476)
[13] http ://www. bio-balance. com/JMGMarticle. pdf
[14] http://www.bio-balance.com/GPCR_Activation.pdf

Computational chemistry 158

Other references

• Christopher J. Cramer Essentials of Computational Chemistry, John Wiley & Sons (2002)

• T. Clark A Handbook of Computational Chemistry, Wiley, New York (1985)

• R. Dronskowski Computational Chemistry of Solid State Materials, Wiley-VCH (2005)

• F. Jensen Introduction to Computational Chemistry, John Wiley & Sons (1999)

• D. Rogers Computational Chemistry Using the PC, 3rd Edition, John Wiley & Sons (2003)

• Paul von Rague Schleyer (Editor-in-Chief). Encyclopedia of Computational Chemistry
(http://eu.wiley.com/WileyCDA/WileyTitle/productCd-047196588X.html). Wiley,
1998. ISBN 0-471-96588-X.

• A. Szabo, N.S. Ostlund, Modern Quantum Chemistry, McGraw-Hill (1982)

• D. Young Computational Chemistry: A Practical Guide for Applying Techniques to Real
World Problems, John Wiley & Sons (2001)

• David Young's Introduction to Computational Chemistry (http://www.ccl.net/cca/
documents/dyoung/topics-orig/compchem.html)

• K.I.Ramachandran, G Deepa and Krishnan Namboori. P.K. Computational Chemistry and
Molecular Modeling Principles and applications (http://www.amrita.edu/cen/

ccmm) Springer- Verlag GmbH ISBN 978-3-540-77302-3

External links

• NIST Computational Chemistry Comparison and Benchmark DataBase (http://srdata.
nist.gov/cccbdb/) - Contains a database of thousands of computational and experimental
results for hundreds of systems

• ACS Division of Computers in Chemistry (http://www.acscomp.org/) - ACS Computers
in Chemistry Division

• Computational Chemistry Wiki (http://www.compchemwiki.org/index.
php?title=Main_Page) - Wiki of computational chemistry results

• CSTB report (http://books.nap.edu/openbook.php?record_id=2206&page=Rl)
Mathematical Research in Materials Science: Opportunities and Perspectives - CSTB
Report

• 3.320 Atomistic Computer Modeling of Materials (SMA 5107) (http://ocw.mit.edu/
OcwWeb/Materials-Science-and-Engineering/3-320Spring-2005/CourseHome/) Free
MIT Course

• Technology Roadmap for Computational Chemistry (http://www.chemicalvision2020.
org/pdfs/compchem.pdf)

• APPLICATIONS OF MOLECULAR AND MATERIALS MODELING, (http://www.wtec.
org/molmodel/mmfinal.pdf)

• Impact of Advances in Computing and Communications Technologies on Chemical
Science and Technology CSTB Report (http://books.nap.edu/openbook.
php?record_id=9591&page=l)

Mathematical chemistry 159

Mathematical chemistry

Mathematical chemistry is the area of research engaged in the novel and nontrivial
applications of mathematics to chemistry; it concerns itself principally with the
mathematical modeling of chemical phenomena. Mathematical chemistry has also
sometimes been called computer chemistry, but should not be confused with
computational chemistry.

Major areas of research in mathematical chemistry include chemical graph theory, which
deals with topics such as the mathematical study of isomerism and the development of
topological descriptors or indices which find application in quantitative structure-property
relationships; chemical aspects of group theory, which finds applications in stereochemistry
and quantum chemistry; and topological aspects of chemistry.

The history of the approach may be traced back into 18th century. Georg Helm published a
treatise titled "The Principles of Mathematical Chemistry: The Energetics of Chemical

[on

Phenomena" in 1894 . Some of the more contemporary periodical publications
specializing in the field are MATCH Communications in Mathematical and in Computer
Chemistry, first published in 1975, and the Journal of Mathematical Chemistry, first
published in 1987.

The basic models for mathematical chemistry are molecular graph and topological index.

See also

• Cheminformatics

• Computational chemistry

• Combinatorial chemistry

• Molecular modeling

Bibliography

• Chemical Applications of Topology and Graph Theory, ed. by R. B. King, Elsevier, 1983.

• Mathematical Concepts in Organic Chemistry, by I. Gutman, O. E. Polansky,
Springer-Verlag, Berlin, 1986.

• Mathematical Chemistry Series, ed. by D. Bonchev, D. H. Rouvray, Gordon and Breach
Science Publisher, Amsterdam, 2000.

Notes

[1] A review (http://links.jstor.org/sici?sici=0036-1445(198806)30:2<348:MCIOC>2.0.CO;2-N&

size=SMALL&origin=JSTOR-reducePage) of the book by Ivan Gutman, Oskar E. Polansky, "Mathematical
Concepts in Organic Chemistry" in SIAM Review Vol. 30, No. 2 (1988), pp. 348-350

[2] Helm, Georg. The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena, translated
by J. Livingston R. Morgan. New York: John Wiley & Sons, 1897. (http://books. google. com/books?hl=en&
id=cyUuAAAAYAAJ&dq=helm+mathematical+chemistry&printsec=frontcover&source=web&
ots=_0vgt-Wots&sig=w4EkV9aqaFd2jb6dXOOs3XObc9o&sa=X&oi=book_result&resnum=l&
ct=result#PPP9,Ml)

Mathematical chemistry 160

References

• N. Trinajstic, I. Gutman, Mathematical Chemistry, Croatica Chemica Acta, 75(2002), pp.
329-356.

• A. T. Balaban, Reflections about Mathematical Chemistry, Foundations of Chemistry,
7(2005), pp. 289-306.

External links

• Journal of Mathematical Chemistry (http://www.springerlink.com/content/101749/)

• MATCH Communications in Mathematical and in Computer Chemistry (http://www.
pmf . kg . ac .yu/match/)

Monte Carlo method

Monte Carlo methods are a class of computational algorithms that rely on repeated
random sampling to compute their results. Monte Carlo methods are often used when
simulating physical and mathematical systems. Because of their reliance on repeated
computation and random or pseudo-random numbers, Monte Carlo methods are most
suited to calculation by a computer. Monte Carlo methods tend to be used when it is
unfeasible or impossible to compute an exact result with a deterministic algorithm.

Monte Carlo simulation methods are especially useful in studying systems with a large
number of coupled degrees of freedom, such as fluids, disordered materials, strongly
coupled solids, and cellular structures (see cellular Potts model). More broadly, Monte
Carlo methods are useful for modeling phenomena with significant uncertainty in inputs,
such as the calculation of risk in business. These methods are also widely used in
mathematics: a classic use is for the evaluation of definite integrals, particularly
multidimensional integrals with complicated boundary conditions. It is a widely successful
method in risk analysis when compared to alternative methods or human intuition. When
Monte Carlo simulations have been applied in space exploration and oil exploration, actual
observations of failures, cost overruns and schedule overruns are routinely better predicted
by the simulations than by human intuition or alternative "soft" methods.

The term "Monte Carlo method" was coined in the 1940s by physicists working on nuclear
weapon projects in the Los Alamos National Laboratory.

Monte Carlo method

161

Overview

There is no single Monte Carlo method; instead, the
term describes a large and widely-used class of
approaches. However, these approaches tend to follow
a particular pattern:

1. Define a domain of possible inputs.

2. Generate inputs randomly from the domain.

3. Perform a deterministic computation using the
inputs.

4. Aggregate the results of the individual computations
into the final result.

For example, the value of n can be approximated using
a Monte Carlo method:

1 . Draw a square on the ground, then inscribe a circle
within it. From plain geometry, the ratio of the area
of an inscribed circle to that of the surrounding
square is n/4.

2. Uniformly scatter some objects of uniform size
throughout the square. For example, grains of rice or
sand.

3. Since the two areas are in the ratio n/4, the objects
should fall in the areas in approximately the same
ratio. Thus, counting the number of objects in the
circle and dividing by the total number of objects in
the square will yield an approximation for n/4.
Multiplying the result by 4 will then yield an
approximation for n itself.

Random shots

Algorithms

°A o

o o

C 1 v

o o

o| o

Outcome

The Monte Carlo method can be

illustrated as a game of battleship.

First a player makes some random

shots. Next the player applies

algorithms (i.e. a battleship is four dots

in the vertical or horizontal direction).

Finally based on the outcome of the

random sampling and the algorithm

the player can determine the likely

locations of the other player's ships.

Notice how the n approximation follows the general

pattern of Monte Carlo algorithms. First, we define a domain of inputs: in this case, it's the
square which circumscribes our circle. Next, we generate inputs randomly (scatter
individual grains within the square), then perform a computation on each input (test
whether it falls within the circle). At the end, we aggregate the results into our final result,
the approximation of n. Note, also, two other common properties of Monte Carlo methods:
the computation's reliance on good random numbers, and its slow convergence to a better
approximation as more data points are sampled. If grains are purposefully dropped into
only, for example, the center of the circle, they will not be uniformly distributed, and so our
approximation will be poor. An approximation will also be poor if only a few grains are
randomly dropped into the whole square. Thus, the approximation of n will become more
accurate both as the grains are dropped more uniformly and as more are dropped.

Monte Carlo method 162

History

The name "Monte Carlo" was popularized by physics researchers Stanislaw Ulam, Enrico
Fermi, John von Neumann, and Nicholas Metropolis, among others; the name is a reference
to the Monte Carlo Casino in Monaco where Ulam's uncle would borrow money to
gamble. The use of randomness and the repetitive nature of the process are analogous to
the activities conducted at a casino.

Random methods of computation and experimentation (generally considered forms of
stochastic simulation) can be arguably traced back to the earliest pioneers of probability
theory (see, e.g., Buffon's needle, and the work on small samples by William Sealy Gosset),
but are more specifically traced to the pre-electronic computing era. The general difference
usually described about a Monte Carlo form of simulation is that it systematically "inverts"
the typical mode of simulation, treating deterministic problems by first finding a
probabilistic analog (see Simulated annealing). Previous methods of simulation and
statistical sampling generally did the opposite: using simulation to test a previously
understood deterministic problem. Though examples of an "inverted" approach do exist
historically, they were not considered a general method until the popularity of the Monte
Carlo method spread.

Perhaps the most famous early use was by Enrico Fermi in 1930, when he used a random
method to calculate the properties of the newly-discovered neutron. Monte Carlo methods
were central to the simulations required for the Manhattan Project, though were severely
limited by the computational tools at the time. Therefore, it was only after electronic
computers were first built (from 1945 on) that Monte Carlo methods began to be studied in
depth. In the 1950s they were used at Los Alamos for early work relating to the
development of the hydrogen bomb, and became popularized in the fields of physics,
physical chemistry, and operations research. The Rand Corporation and the U.S. Air Force
were two of the major organizations responsible for funding and disseminating information
on Monte Carlo methods during this time, and they began to find a wide application in
many different fields.

Uses of Monte Carlo methods require large amounts of random numbers, and it was their
use that spurred the development of pseudorandom number generators, which were far
quicker to use than the tables of random numbers which had been previously used for
statistical sampling.

Applications

As mentioned, Monte Carlo simulation methods are especially useful for modeling
phenomena with significant uncertainty in inputs and in studying systems with a large
number of coupled degrees of freedom. Specific areas of application include:

Physical sciences

Monte Carlo methods are very important in computational physics, physical chemistry, and
related applied fields, and have diverse applications from complicated quantum
chromodynamics calculations to designing heat shields and aerodynamic forms. The Monte
Carlo method is widely used in statistical physics, in particular, Monte Carlo molecular
modeling as an alternative for computational molecular dynamics; see Monte Carlo method
in statistical physics. In experimental particle physics, these methods are used for

Monte Carlo method 163

designing detectors, understanding their behavior and comparing experimental data to
theory.

Monte Carlo methods are also used in the ensemble models that form the basis of modern
weather forecasting operations.

Design and visuals

Monte Carlo methods have also proven efficient in solving coupled integral differential
equations of radiation fields and energy transport, and thus these methods have been used
in global illumination computations which produce photorealistic images of virtual 3D
models, with applications in video games, architecture, design, computer generated films,
special effects in cinema.

Finance and business

Monte Carlo methods in finance are often used to calculate the value of companies, to
evaluate investments in projects at corporate level or to evaluate financial derivatives. The
Monte Carlo method is intended for financial analysts who want to construct stochastic or
probabilistic financial models as opposed to the traditional static and deterministic models.
For its use in the insurance industry, see stochastic modelling.

Telecommunications

When planning a wireless network, design must be proved to work for a wide variety of
scenarios that depend mainly on the number of users, their locations and the services they
want to use. Monte Carlo methods are typically used to generate these users and their
states. The network performance is then evaluated and, if results are not satisfactory, the
network design goes through an optimization process.

Games

Monte Carlo methods have recently been applied in game playing related artificial
intelligence theory. Most notably the game of Go has seen remarkably successful Monte
Carlo algorithm based computer players. One of the main problems that this approach has
in game playing is that it sometimes misses an isolated, very good move. These approaches
are often strong strategically but weak tactically, as tactical decisions tend to rely on a
small number of crucial moves which are easily missed by the randomly searching Monte
Carlo algorithm.

Monte Carlo simulation versus "what if" scenarios

The opposite of Monte Carlo simulation might be considered deterministic modeling using
single-point estimates. Each uncertain variable within a model is assigned a "best guess"
estimate. Various combinations of each input variable are manually chosen (such as best
case, worst case, and most likely case), and the results recorded for each so-called "what if"
scenario.

By contrast, Monte Carlo simulation considers random sampling of probability distribution
functions as model inputs to produce hundreds or thousands of possible outcomes instead

of a few discrete scenarios. The results provide probabilities of different outcomes
occurring. For example, a comparison of a spreadsheet cost construction model run
using traditional "what if" scenarios, and then run again with Monte Carlo simulation and

Monte Carlo method 1 64

Triangular probability distributions shows that the Monte Carlo analysis has a narrower
range than the "what if" analysis. This is because the "what if" analysis gives equal weight
to all scenarios. ^

For an application, see quantifying uncertainty under corporate finance.

Use in mathematics

In general, Monte Carlo methods are used in mathematics to solve various problems by
generating suitable random numbers and observing that fraction of the numbers obeying
some property or properties. The method is useful for obtaining numerical solutions to
problems which are too complicated to solve analytically. The most common application of
the Monte Carlo method is Monte Carlo integration.

Integration

Deterministic methods of numerical integration operate by taking a number of evenly
spaced samples from a function. In general, this works very well for functions of one
variable. However, for functions of vectors, deterministic quadrature methods can be very
inefficient. To numerically integrate a function of a two-dimensional vector, equally spaced
grid points over a two-dimensional surface are required. For instance a 10x10 grid requires
100 points. If the vector has 100 dimensions, the same spacing on the grid would require
10 points— far too many to be computed. 100 dimensions is by no means unreasonable,
since in many physical problems, a "dimension" is equivalent to a degree of freedom. (See
Curse of dimensionality.)

Monte Carlo methods provide a way out of this exponential time-increase. As long as the
function in question is reasonably well-behaved, it can be estimated by randomly selecting
points in 100-dimensional space, and taking some kind of average of the function values at
these points. By the law of large numbers, this method will display 1/vJV
convergence— i.e. quadrupling the number of sampled points will halve the error,
regardless of the number of dimensions.

A refinement of this method is to somehow make the points random, but more likely to
come from regions of high contribution to the integral than from regions of low
contribution. In other words, the points should be drawn from a distribution similar in form
to the integrand. Understandably, doing this precisely is just as difficult as solving the
integral in the first place, but there are approximate methods available: from simply making
up an integrable function thought to be similar, to one of the adaptive routines discussed in
the topics listed below.

A similar approach involves using low-discrepancy sequences instead— the quasi-Monte
Carlo method. Quasi-Monte Carlo methods can often be more efficient at numerical
integration because the sequence "fills" the area better in a sense and samples more of the
most important points that can make the simulation converge to the desired solution more
quickly.

Monte Carlo method 165

Integration methods

• Direct sampling methods

• Importance sampling

• Stratified sampling

• Recursive stratified sampling

• VEGAS algorithm

• Random walk Monte Carlo including Markov chains

• Metropolis-Hastings algorithm

• Gibbs sampling

Optimization

Another powerful and very popular application for random numbers in numerical simulation
is in numerical optimization. These problems use functions of some often large-dimensional
vector that are to be minimized (or maximized). Many problems can be phrased in this way:
for example a computer chess program could be seen as trying to find the optimal set of,
say, 10 moves which produces the best evaluation function at the end. The traveling
salesman problem is another optimization problem. There are also applications to
engineering design, such as multidisciplinary design optimization.

Most Monte Carlo optimization methods are based on random walks. Essentially, the
program will move around a marker in multi-dimensional space, tending to move in
directions which lead to a lower function, but sometimes moving against the gradient.

Optimization methods

• Evolution strategy

• Genetic algorithms

• Parallel tempering

• Simulated annealing

• Stochastic optimization

• Stochastic tunneling

Inverse problems

Probabilistic formulation of inverse problems leads to the definition of a probability
distribution in the model space. This probability distribution combines a priori information
with new information obtained by measuring some observable parameters (data). As, in the
general case, the theory linking data with model parameters is nonlinear, the a posteriori
probability in the model space may not be easy to describe (it may be multimodal, some
moments may not be defined, etc.).

When analyzing an inverse problem, obtaining a maximum likelihood model is usually not
sufficient, as we normally also wish to have information on the resolution power of the data.
In the general case we may have a large number of model parameters, and an inspection of
the marginal probability densities of interest may be impractical, or even useless. But it is
possible to pseudorandomly generate a large collection of models according to the posterior
probability distribution and to analyze and display the models in such a way that
information on the relative likelihoods of model properties is conveyed to the spectator.
This can be accomplished by means of an efficient Monte Carlo method, even in cases
where no explicit formula for the a priori distribution is available.

Monte Carlo method 166

The best-known importance sampling method, the Metropolis algorithm, can be
generalized, and this gives a method that allows analysis of (possibly highly nonlinear)
inverse problems with complex a priori information and data with an arbitrary noise
distribution. For details, see Mosegaard and Tarantola (1995), or Tarantola (2005).

Computational mathematics

Monte Carlo methods are useful in many areas of computational mathematics, where a
lucky choice can find the correct result. A classic example is Rabin's algorithm for primality
testing: for any n which is not prime, a random x has at least a 75% chance of proving that
n is not prime. Hence, if n is not prime, but x says that it might be, we have observed at
most a l-in-4 event. If 10 different random x say that "n is probably prime" when it is not,
we have observed a one-in-a-million event. In general a Monte Carlo algorithm of this kind
produces one correct answer with a guarantee n is composite, and x proves it so, but
another one without, but with a guarantee of not getting this answer when it is wrong too
often — in this case at most 25% of the time. See also Las Vegas algorithm for a related,
but different, idea.

Monte Carlo and random numbers

Interestingly, Monte Carlo simulation methods do not always require truly random numbers
to be useful — while for some applications, such as primality testing, unpredictability is
vital (see Davenport (1995)). Many of the most useful techniques use deterministic,
pseudo-random sequences, making it easy to test and re-run simulations. The only quality
usually necessary to make good simulations is for the pseudo-random sequence to appear
"random enough" in a certain sense.

What this means depends on the application, but typically they should pass a series of
statistical tests. Testing that the numbers are uniformly distributed or follow another
desired distribution when a large enough number of elements of the sequence are
considered is one of the simplest, and most common ones.

See also

General

Auxiliary field Monte Carlo
Bootstrapping (statistics)
Demon algorithm
Evolutionary Computation
Las Vegas algorithm
Markov chain
Molecular dynamics
Monte Carlo option model
Monte Carlo integration
Quasi-Monte Carlo method
Random number generator
Randomness
Resampling (statistics)

Monte Carlo method 167

Application areas

• Graphics, particularly for ray tracing; a version of the Metropolis-Hastings algorithm is
also used for ray tracing where it is known as Metropolis light transport
Modeling light transport in biological tissue
Monte Carlo methods in finance
Reliability engineering

In simulated annealing for protein structure prediction

In semiconductor device research, to model the transport of current carriers
Environmental science, dealing with contaminant behavior

Search And Rescue and Counter-Pollution. Models used to predict the drift of a life raft
or movement of an oil slick at sea.

In probabilistic design for simulating and understanding the effects of variability
In physical chemistry, particularly for simulations involving atomic clusters
In biomolecular simulations
In polymer physics

• Bond fluctuation model
In computer science

• Las Vegas algorithm

• LURCH

• Computer go

• General Game Playing

Modeling the movement of impurity atoms (or ions) in plasmas in existing and tokamaks
(e.g.: DIVIMP).
Nuclear and particle physics codes using the Monte Carlo method:

GEANT — CERN's simulation of high energy particles interacting with a detector.
CompHEP, PYTHIA — Monte-Carlo generators of particle collisions
MCNP(X) - LANL's radiation transport codes

MCU: universal computer code for simulation of particle transport (neutrons, photons,
electrons) in three-dimensional systems by means of the Monte Carlo method
EGS — Stanford's simulation code for coupled transport of electrons and photons
PEREGRINE: LLNL's Monte Carlo tool for radiation therapy dose calculations
BEAMnrc — Monte Carlo code system for modeling radiotherapy sources (LINAC's)
PENELOPE — Monte Carlo for coupled transport of photons and electrons, with
applications in radiotherapy

• MONK — Serco Assurance's code for the calculation of k-effective of nuclear systems
Modelling of foam and cellular structures
Modeling of tissue morphogenesis
Computation of holograms
Phylogenetic analysis, i.e. Bayesian inference, Markov chain Monte Carlo

Monte Carlo method 168

Other methods employing Monte Carlo

Assorted random models, e.g. self-organised criticality

Direct simulation Monte Carlo

Dynamic Monte Carlo method

Kinetic Monte Carlo

Quantum Monte Carlo

Quasi-Monte Carlo method using low-discrepancy sequences and self avoiding walks

Semiconductor charge transport and the like

Electron microscopy beam-sample interactions

Stochastic optimization

Cellular Potts model

Markov chain Monte Carlo

Cross-entropy method

Applied information economics

Monte Carlo localization

Notes

[1] Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business" pg. 46, John Wiley

& Sons, 2007
[2] Douglas Hubbard "The Failure of Risk Management: Why It's Broken and How to Fix It", John Wiley & Sons,

2009
[3] Nicholas Metropolis (1987), "http://library.lanl.gov/la-pubs/00326866.pdflThe beginning of the Monte Carlo

method", Los Alamos Science (1987 Special Issue dedicated to Stanislaw Ulam): 125-130, http://library.lanl.

gov/la-pubs/00326866.pdf
[4] Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business" pg. 46, John Wiley

& Sons, 2007
[5] David Vose: "Risk Analysis, A Quantitative Guide," Second Edition, p. 13, John Wiley & Sons, 2000.
[6] Ibid, p. 16

[7] Ibid, p. 17, showing graph

[8] http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Papers_PDF/MonteCarlo_latex.pdf
[9] http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/SIAM/index.html
[10] Davenport, J. H.. http://doi.acm.Org/10.l 145/143242. 143290|"Primality testing revisited", doi:

http://doi.acm.org/10.1145/143242.143290 (http://dx.doi.Org/http://doi.acm.org/10.1145/143242.

143290). http://doi.acm.org/10.1145/143242.143290. Retrieved on 2007-08-19.

References

• Metropolis, N.; Ulam, S. (1949). "The Monte Carlo Method". Journal of the American
Statistical Association 44 (247): 335-341. doi: 10.2307/2280232 (http://dx.doi.org/10.
2307/2280232).

• Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.; Teller, Augusta
H.; Teller, Edward (1953). "Equation of State Calculations by Fast Computing Machines".
Journal of Chemical Physics 21 (6): 1087. doi: 10.1063/1.1699114 (http://dx.doi.org/

10.1063/1.1699114).

• Hammersley, J. M.; Handscomb, D. C. (1975). Monte Carlo Methods. London: Methuen.
ISBN 0416523404.

• Kahneman, D.; Tversky, A. (1982). Judgement under Uncertainty: Heuristics and Biases.
Cambridge University Press.

• Gould, Harvey; Tobochnik, Jan (1988). An Introduction to Computer Simulation Methods,
Part 2, Applications to Physical Systems. Reading: Addison-Wesley. ISBN 020116504X.

Monte Carlo method 169

Binder, Kurt (1995). The Monte Carlo Method in Condensed Matter Physics. New York:

Springer. ISBN 0387543694.

Berg, Bernd A. (2004). Markov Chain Monte Carlo Simulations and Their Statistical

Analysis (With Web-Based Fortran Code). Hackensack, NJ: World Scientific. ISBN

9812389350.

Caflisch, R. E. (1998). Monte Carlo and quasi-Monte Carlo methods. Acta Numerica. 7.

Cambridge University Press, pp. 1-49.

Doucet, Arnaud; Freitas, Nando de; Gordon, Neil (2001). Sequential Monte Carlo

methods in practice. New York: Springer. ISBN 0387951466.

Fishman, G. S. (1995). Monte Carlo: Concepts, Algorithms, and Applications. New York:

Springer. ISBN 038794527X.

MacKeown, P. Kevin (1997). Stochastic Simulation in Physics. New York: Springer. ISBN

9813083263.

Robert, C. P.; Casella, G. (2004). Monte Carlo Statistical Methods (2nd ed.). New York:

Springer. ISBN 0387212396.

Rubinstein, R. Y.; Kroese, D. P. (2007). Simulation and the Monte Carlo Method (2nd ed.).

New York: John Wiley & Sons. ISBN 9780470177938.

Mosegaard, Klaus; Tarantola, Albert (1995). "Monte Carlo sampling of solutions to

inverse problems". J. Geophys. Res. 100 (B7): 12431-12447. doi: 10.1029/94JB03097

(http://dx.doi.org/10.1029/94JB03097).

Tarantola, Albert (2005).

http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/SIAM/index.html\Inverse

Problem Theory. Philadelphia: Society for Industrial and Applied Mathematics. ISBN

0898715725. http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/SIAM/index.

html.

External links

Overview and reference list (http://mathworld.wolfram.com/MonteCarloMethod.

html), Mathworld

Introduction to Monte Carlo Methods (http://www.ipp.mpg.de/de/for/bereiche/

stellarator/Compsci/CompScience/csep/csepl.phy. ornl.gov/mc/mc. html),

Computational Science Education Project

Overview of formulas used in Monte Carlo simulation (http://www.sitmo.com/eqcat/

15), the Quant Equation Archive, at sitmo.com

The Basics of Monte Carlo Simulations (http://www.chem.unl.edu/zeng/joy/mclab/

mcintro.html), University of Nebraska-Lincoln

Introduction to Monte Carlo simulation (http://office.microsoft.com/en-us/assistance/

HA011118931033.aspx) (for Excel), Wayne L. Winston

Monte Carlo Methods - Overview and Concept (http://www.brighton-webs.co.uk/

montecarlo/concept.asp), brighton-webs.co.uk

Molecular Monte Carlo Intro (http://www.cooper.edu/engineering/chemechem/

monte.html), Cooper Union

Monte Carlo techniques applied in physics (http://homepages.ed.ac.uk/s0095122/

Appletl-page.htm)

MonteCarlo Simulation in Finance (http://www.global-derivatives.com/maths/k-o.

php), global-derivatives.com

Monte Carlo method 170

• Approximation of n with the Monte Carlo Method (http://twt.mpei.ac.ru/MAS/
Worksheets/approxpi.mcd)

• Risk Analysis in Investment Appraisal (http://papers.ssrn.com/sol3/papers.
cfm?abstract_id=265905), The Application of Monte Carlo Methodology in Project
Appraisal, Sawakis C. Sawides

• Probabilistic Assessment of Structures using the Monte Carlo method (http://en.
wikiversity.org/wiki/Probabilistic_Assessment_of_Structures), Wikiuniversity paper for
students of Structural Engineering

• A very intuitive and comprehensive introduction to Quasi-Monte Carlo methods (http://
www.puc-rio.br/marco.ind/quasi_mc.html)

• Pricing using Monte Carlo simulation (http://knol.google.eom/k/giancarlo-vercellino/
pricing-using-monte-carlo-simulation/lld5i2rgd9gn5/3#) / a practical example, Prof.
Giancarlo Vercellino

Software

• The BUGS project (http://www.mrc-bsu.cam.ac.uk/bugs/) (including WinBUGS and
OpenBUGS)

• Monte Carlo Simulation, Resampling, Bootstrap tool (http://www.statisticsl01.net)

• YASAI: Yet Another Simulation Add-In (http://yasai.rutgers.edu/) - Free Monte Carlo
Simulation Add-In for Excel created by Rutgers University

Quantum Monte Carlo

Electronic structure methods

Tight binding
Nearly-free electron model

Hartree-Fock
Modern valence bond

Generalized valence bond
Moller-Plesset perturbation theory

Configuration interaction
Coupled cluster

Multi-configurational self-consistent field
Density functional theory

Quantum chemistry composite methods
Quantum Monte Carlo

kp perturbation theory
Muffin-tin approximation

LCAO method

Quantum Monte Carlo is a large class of computer algorithms that simulate quantum
systems with the idea of solving the many-body problem. They use, in one way or another,
the Monte Carlo method to handle the many-dimensional integrals that arise. Quantum

Quantum Monte Carlo 171

Monte Carlo allows a direct representation of many-body effects in the wavefunction, at the
cost of statistical uncertainty that can be reduced with more simulation time. For bosons,
there exist numerically exact and polynomial-scaling algorithms. For fermions, there exist
very good approximations and numerically exact exponentially scaling quantum Monte
Carlo algorithms, but none that are both.

Background

In principle, any physical system can be described by the many-body Schrodinger equation
as long as the constituent particles are not moving "too" fast; that is, they are not moving
near the speed of light. This includes the electrons in almost every material in the world, so
if we could solve the Schrodinger equation, we could predict the behavior of any electronic
system, which has important applications in fields from computers to biology. This also
includes the nuclei in Bose-Einstein condensate and superfluids such as liquid helium. The
difficulty is that the Schrodinger equation involves a function of three times the number of
particles and is difficult to solve even using parallel computing technology in a reasonable
amount of time (less than 2 years). Traditionally, theorists have approximated the
many-body wave function as an antisymmetric function of one-body orbitals, as shown
concisely at this link. This kind of formulation either limits the possible wave functions, as
in the case of the Hartree-Fock (HF) approximation, or converges very slowly, as in
configuration interaction. One of the reasons for the difficulty with an HF initial estimate
(ground state seed, also known as Slater determinant) is that it is very difficult to model the
electronic and nuclear cusps in the wavefunction. However, one does not generally model
at this point of the approximation. As two particles approach each other, the wavefunction
has exactly known derivatives.

Quantum Monte Carlo is a way around these problems because it allows us to model a
many-body wavefunction of our choice directly. Specifically, we can use a Hartree-Fock
approximation as our starting point but then multiplying it by any symmetric function, of
which Jastrow functions are typical, designed to enforce the cusp conditions. Most methods
aim at computing the ground-state wavefunction of the system, with the exception of path
integral Monte Carlo and finite-temperature auxiliary field Monte Carlo, which calculate the
density matrix.

There are several quantum Monte Carlo methods, each of which uses Monte Carlo in
different ways to solve the many-body problem:

Quantum Monte Carlo methods

• Variational Monte Carlo : A good place to start; it is commonly used in many sorts of
quantum problems.

• Diffusion Monte Carlo : The most common high-accuracy method for electrons (that is,
chemical problems), since it comes quite close to the exact ground-state energy fairly
efficiently. Also used for simulating the quantum behavior of atoms, etc.

• Path integral Monte Carlo : Finite-temperature technique mostly applied to bosons where
temperature is very important, especially superfluid helium.

• Auxiliary field Monte Carlo : Usually applied to lattice problems, although there has been
recent work on applying it to electrons in chemical systems.

• Reptation Monte Carlo : Recent zero-temperature method related to path integral Monte
Carlo, with applications similar to diffusion Monte Carlo but with some different

Quantum Monte Carlo 172

tradeoffs.

• Gaussian quantum Monte Carlo

See also

Stochastic Green Function (SGF) algorithm

Monte Carlo method

QMC@Home

Quantum chemistry

Density matrix renormalization group

Time-evolving block decimation

Metropolis algorithm

Wavefunction optimization

References

[ 1 ] http ://www. attaccalite. altervista. org/PhDThesis/html/node9.html

• Hammond, B.J.; W.A. Lester & P.J. Reynolds (1994) (in English).
http://www.worldscibooks.com/chemistry/ll 70 .html\Monte Carlo Methods in Ab Initio
Quantum Chemistry. Singapore: World Scientific. ISBN 981-02-0321-7. OCLC 29594695
(http://worldcat.org/oclc/29594695). http://www.worldscibooks.com/chemistry/
1170.html. Retrieved on 2007-01-18.

• Nightingale, M.P.; Umrigar, Cyrus J., ed (1999) (in English).
http://www. springer. com/west/0-7923-5552-0\Quantum Monte Carlo Methods in Physics
and Chemistry. Springer. ISBN 978-0-7923-5552-6. http://www.springer.com/west/
0-7923-5552-0. Retrieved on 2007-01-18.

• W. M. C. Foulkes; L. Mitas, R. J. Needs and G. Rajagopal (5 January 2001).
"http://link.aps.org/abstract/RMP/v73/p33IQuantum Monte Carlo simulations of solids" (in
English) (abstract). Rev. Mod. Phys. 73: 33-83. doi: 10.1103/RevModPhys.73.33 (http://
dx.doi.org/10.1103/RevModPhys.73.33). http://link.aps.org/abstract/RMP/v73/
p33. Retrieved on 2007-01-18.

• Raimundo R. dos Santos (2003). "http://arxiv.org/abs/cond-mat/0303551vlllntroduction
to Quantum Monte Carlo simulations for fermionic systems" (in English) (fulltext). Braz.
J. Phys. 33: 36. http://arxiv.org/abs/cond-mat/0303551vl. Retrieved on 2007-01-18.

External links

• QMCWIKI (http://www.qmcwiki.org/)

• Joint DEMOCRITOS-ICTP School on Continuum Quantum Monte Carlo Methods (http://
cdsagenda5.ictp.trieste.it/full_display.php?ida=a0332&fid=)

• FreeScience Library -> Quantum Monte Carlo (http://freescience.info/books.
php?id=35)

• UIUC 2007 Summer School on Computational Materials Science: Quantum Monte Carlo
from Minerals and Materials to Molecules (http://www.mcc.uiuc.edu/summerschool/
2007/qmc/)

• Quantum Monte Carlo in the Apuan Alps V (http://www.vallico.net/tti/tti.html) -
international workshop, Vallico Sotto, Tuscany, 25 July-1 August 2009 (Click PUBLIC
EVENTS) - Announcement (http://www.vallico.net/tti/qmcitaa_09/announcement.
html), Poster (http://www.tcm.phy.cam.ac.uk/~mdt26/tti2/poster/

Quantum Monte Carlo 173

tti_c_poster_2009.png)
• Quantum Monte Carlo and the CASINO program IV (http://www.vallico.net/tti/tti.

html) - summer school, Vallico Sotto, Tuscany, 2-9 August 2009 (Click PUBLIC EVENTS) -
Announcement (http://www.vallico.net/tti/qmcatcp_09/announcement.html), Poster
(http://www.tcm.phy.cam.ac.uk/~mdt26/tti2/poster/tti_ss_poster_2009.png)

Dynamics of Markovian particles

Dynamics of Markovian particles (or DMP) is the basis of a theory for kinetics of
particles in open heterogeneous systems. It can be looked upon as an application of the
notion of stochastic process conceived as a physical entity; e.g. the particle moves because
there is a transition probability acting on it.

Two particular features of DMP might be noticed: (1) an ergodic like relation between the
motion of particle and the corresponding steady state, and (2) the classic notion of
geometric volume appears nowhere (e.g. a concept such as flow of "substance" is not
expressed as liters per time unit but as number of particles per time unit). Though being
primitive DMP has been applied for solving a classic paradox of the absorption of mercury
by fish and by mollusks. The theory has also been applied for a purely probabilistic
derivation of the fundamental physical principle: conservation of mass; this might be looked
upon as a contribution to the old and ongoing discussion of the relation between physics
and probability theory.

Sources

• Bergner— DMP, a kinetics of macroscopic particles in open heterogeneous systems

References

[ 1 ] http :// www. bergner. se/DMP/download. htm

Dynamics of Markovian particles 1 74

Molecular Networks and Complex
Molecule Dynamics

Metabolic network

A metabolic network is the complete set of metabolic and physical processes that
determine the physiological and biochemical properties of a cell. As such, these networks
comprise the chemical reactions of metabolism as well as the regulatory interactions that
guide these reactions.

With the sequencing of complete genomes, it is now possible to reconstruct the network of
biochemical reactions in many organisms, from bacteria to human. Several of these
networks are available online: Kyoto Encyclopedia of Genes and Genomes (KEGG)[1],
EcoCyc [2] and BioCyc [3]. Metabolic networks are powerful tools, for studying and
modelling metabolism. From the study of metabolic networks' topology with graph theory to
predictive toxicology and ADME.

See also

• Metabolic network modelling

• Metabolic pathway

References

[1] http://www.genome.ad.jp
[2] http://www.ecocyc.org
[3] http://biocyc.org

Topological dynamics 175

Topological dynamics

In mathematics, topological dynamics is a branch of the theory of dynamical systems in
which qualitative, asymptotic properties of dynamical systems are studied from the
viewpoint of general topology.

Scope

The central object of study in topological dynamics is a topological dynamical system,

i.e. a topological space, together with a continuous transformation, a continuous flow, or
more generally, a semigroup of continuous transformations of that space. The origins of
topological dynamics lie in the study of asymptotical properties of trajectories of systems of
autonomous ordinary differential equations, in particular, the behavior of limit sets and
various manifestations of "repetetiveness" of the motion, such as periodic trajectories,
recurrence and minimality, stability, non-wandering points. George Birkhoff is considered
to be the founder of the field. A structure theorem for minimal distal flows proved by Hillel
Furstenberg in the early 1960s inspired much work on classification of minimal flows. A lot
of research in the 1970s and 1980s was devoted to topological dynamics of one-dimensional
maps, in particular, piecewise linear self-maps of the interval and the circle.

Unlike the theory of smooth dynamical systems, where the main object of study is a smooth
manifold with a diffeomorphism or a smooth flow, phase spaces considered in topological
dynamics are general metric spaces (usually, compact). This necessitates development of
entirely different techniques but allows extra degree of flexibility even in the smooth
setting, because invariant subsets of a manifold are frequently very complicated
topologically (cf limit cycle, strange attractor); additionally, shift spaces arising via
symbolic representations can be considered on an equal footing with more geometric
actions. Topological dynamics has intimate connections with ergodic theory of dynamical
systems, and many fundamental concepts of the latter have topological analogues (cf
Kolmogorov-Sinai entropy and topological entropy).

See also

• Poincare-Bendixson theorem

• Symbolic dynamics

• Topological conjugacy

References

• D.V.Anosov (2001), http://eom.springer.de/T/t093030.htm|"Topological dynamics", in
Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN
978-1556080104

• Topological dynamics at Scholarpedia, curated by Joseph Auslander.

• Robert Ellis, Lectures on topological dynamics. W. A. Benjamin, Inc., New York 1969

• Walter Gottschalk, Gustav Hedlund, Topological dynamics. American Mathematical
Society Colloquium Publications, Vol. 36. American Mathematical Society, Providence, R.
I., 1955

Topological dynamics

176

• J. de Vries, Elements of topological dynamics. Mathematics and its Applications, 257.
Kluwer Academic Publishers Group, Dordrecht, 1993 ISBN 0-7923-2287-8

References

[ 1 ] http ://www. scholarpedia. org/article/Topologicaldynamics

Protein folding

Protein before and after folding.

Protein folding is the physical

process by which a polypeptide

folds into its characteristic and

functional three-dimensional

structure from random coil. 1 J

Each protein exists as an unfolded

polypeptide or random coil when

translated from a sequence of

mRNA to a linear chain of amino

acids. This polypeptide lacks any

developed three-dimensional

structure (the left hand side of the neighboring figure). However amino acids interact with

each other to produce a well-defined three dimensional structure, the folded protein (the

right hand side of the figure), known as the native state. The resulting three-dimensional

structure is determined by the amino acid sequence. ^ .

For many proteins the correct three dimensional structure is essential to function. Failure
to fold into the intended shape usually produces inactive proteins with different properties
including toxic prions. Several neurodegenerative and other diseases are believed to result
from the accumulation of misfolded (incorrectly folded) proteins.

Protein folding

177

Known facts about the process

The relationship between folding and amino acid sequence

The amino-acid sequence (or
primary structure) of a protein
defines its native conformation. A
protein molecule folds

spontaneously during or after
synthesis. While these

macromolecules may be regarded
as "folding themselves", the
process also depends on the
solvent (water or lipid bilayer)/ '
the concentration of salts, the
temperature, and the presence of
molecular chaperones.

Folded proteins usually have a
hydrophobic core in which side
chain packing stabilizes the folded
state, and charged or polar side
chains occupy the solvent-exposed
surface where they interact with
surrounding water. Minimizing the
number of hydrophobic side-chains

Illustration of the main driving force behind protein structure

formation. In the compact fold (to the right), the hydrophobic

amino acids (shown as black spheres) are in general shielded

from the solvent.

[6]

exposed to water is an important driving force behind the folding process, . Formation of
intramolecular hydrogen bonds provides another important contribution to protein

T71

stability. The strength of hydrogen bonds depends on their environment, thus H-bonds
enveloped in a hydrophobic core contribute more than H-bonds exposed to the aqueous
environment to the stability of the native state.

The process of folding in vivo often begins co-translationally, so that the N-terminus of the
protein begins to fold while the C-terminal portion of the protein is still being synthesized
by the ribosome. Specialized proteins called chaperones assist in the folding of other
proteins. A well studied example is the bacterial GroEL system, which assists in the
folding of globular proteins. In eukaryotic organisms chaperones are known as heat shock
proteins. Although most globular proteins are able to assume their native state unassisted,
chaperone-assisted folding is often necessary in the crowded intracellular environment to
prevent aggregation; chaperones are also used to prevent misfolding and aggregation
which may occur as a consequence of exposure to heat or other changes in the cellular
environment.

For the most part, scientists have been able to study many identical molecules folding
together en masse. At the coarsest level, it appears that in transitioning to the native state,
a given amino acid sequence takes on roughly the same route and proceeds through
roughly the same intermediates and transition states. Often folding involves first the
establishment of regular secondary and supersecondary structures, particularly alpha
helices and beta sheets, and afterwards tertiary structure. Formation of quaternary

Protein folding 178

structure usually involves the "assembly" or "coassembly" of subunits that have already
folded. The regular alpha helix and beta sheet structures fold rapidly because they are
stabilized by intramolecular hydrogen bonds, as was first characterized by Linus Pauling.
Protein folding may involve covalent bonding in the form of disulfide bridges formed
between two cysteine residues or the formation of metal clusters. Shortly before settling
into their more energetically favourable native conformation, molecules may pass through
an intermediate "molten globule" state.

The essential fact of folding, however, remains that the amino acid sequence of each
protein contains the information that specifies both the native structure and the pathway to
attain that state. This is not to say that nearly identical amino acid sequences always fold
similarly. Conformations differ based on environmental factors as well; similar proteins
fold differently based on where they are found. Folding is a spontaneous process
independent of energy inputs from nucleoside triphosphates. The passage of the folded
state is mainly guided by hydrophobic interactions, formation of intramolecular hydrogen
bonds, and van der Waals forces, and it is opposed by conformational entropy.

Disruption of the native state

Under some conditions proteins will not fold into their biochemically functional forms.
Temperatures above or below the range that cells tend to live in will cause thermally
unstable proteins to unfold or "denature" (this is why boiling makes an egg white turn
opaque). High concentrations of solutes, extremes of pH, mechanical forces, and the
presence of chemical denaturants can do the same. A fully denatured protein lacks both
tertiary and secondary structure, and exists as a so-called random coil. Under certain
conditions some proteins can refold; however, in many cases denaturation is
irreversible. Cells sometimes protect their proteins against the denaturing influence of
heat with enzymes known as chaperones or heat shock proteins, which assist other proteins
both in folding and in remaining folded. Some proteins never fold in cells at all except with
the assistance of chaperone molecules, which either isolate individual proteins so that their
folding is not interrupted by interactions with other proteins or help to unfold misfolded
proteins, giving them a second chance to refold properly. This function is crucial to prevent
the risk of precipitation into insoluble amorphous aggregates.

Incorrect protein folding and neurodegenerative disease

Aggregated proteins are associated with prion-related illnesses such as Creutzfeldt-Jakob
disease, bovine spongiform encephalopathy (mad cow disease), amyloid-related illnesses
such as Alzheimer's Disease and familial amyloid cardiomyopathy or polyneuropathy, as
well as intracytoplasmic aggregation diseases such as Huntington's and Parkinson's
disease. These age onset degenerative diseases are associated with the multimerization of
misfolded proteins into insoluble, extracellular aggregates and/or intracellular inclusions
including cross-beta sheet amyloid fibrils; it is not clear whether the aggregates are the
cause or merely a reflection of the loss of protein homeostasis, the balance between
synthesis, folding, aggregation and protein turnover. Misfolding and excessive degradation
instead of folding and function leads to a number of proteopathy diseases such as
antitrypsin-associated Emphysema, cystic fibrosis and the lysosomal storage diseases,
where loss of function is the origin of the disorder. While protein replacement therapy has
historically been used to correct the latter disorders, an emerging approach is to use
pharmaceutical chaperones to fold mutated proteins to render them functional. Chris

Protein folding 179

Dobson, Jeffery W. Kelly, Dennis Selkoe, Stanley Prusiner, Peter T. Lansbury, William E.
Balch, Richard I. Morimoto, Susan L. Lindquist and Byron C. Caughey have all contributed
to this emerging understanding of protein-misfolding diseases.

Kinetics and the Levinthal Paradox

The duration of the folding process varies dramatically depending on the protein of interest.
When studied outside the cell, the slowest folding proteins require many minutes or hours
to fold primarily due to proline isomerization, and must pass through a number of

ri 21

intermediate states, like checkpoints, before the process is complete. On the other hand,
very small single-domain proteins with lengths of up to a hundred amino acids typically fold

ri on

in a single step. Time scales of milliseconds are the norm and the very fastest known
protein folding reactions are complete within a few microseconds.

The Levinthal paradox observes that if a protein were to fold by sequentially sampling all
possible conformations, it would take an astronomical amount of time to do so, even if the
conformations were sampled at a rapid rate (on the nanosecond or picosecond scale). Based
upon the observation that proteins fold much faster than this, Levinthal then proposed that
a random conformational search does not occur, and the protein must, therefore, fold
through a series of meta-stable intermediate states.

Techniques for studying protein folding

Circular Dichroism

Circular dichroism is one of the most general and basic tools to study protein folding.
Circular dichroism spectroscopy measures the absorption of circularly polarized light. In
proteins, structures such as alpha helicies and beta sheets are chiral, and thus absorb such
light. The absorption of this light acts as a marker of the degree of foldedness of the protein
ensemble. This technique can be used to measure equilibrium unfolding of the protein by
measuring the change in this absorption as a function of denaturant concentration or
temperature. A denaturant melt measures the free energy of unfolding as well as the
protein's m value, or denaturant dependence. A temperature melt measures the melting
temperature (T ) of the protein. This type of spectroscopy can also be combined with
fast-mixing devices, such as stopped flow, to measure protein folding kinetics and to
generate chevron plots.

Dual Polarisation Interferometry

Dual Polarisation Interferometry is a relatively new benchtop technique for measuring the
overall change in protein size and fold density during interactions or other stimulus. The
technique captures a layer of protein on a glass slide and, using two polarisations of light,
measures the conformation and conformational changes with a time resolution of circa
10Hz at a dimensional resolution of O.Olnm. The method is quantitative and can be
compared directly to what one would expect of crystallography data.

Protein folding 180

Vibrational circular dichroism of proteins

The more recent developments of vibrational circular dichroism (VCD) techniques for
proteins, currently involving Fourier transform (FFT) instruments, provide powerful means
for determining protein conformations in solution even for very large protein molecules.
Such VCD studies of proteins are often combined with X-ray diffraction of protein crystals,
FT-IR data for protein solutions in heavy water (DO), or ab initio quantum computations to
provide unambiguous structural assignments that are unobtainable from CD.

Modern studies of folding with high time resolution

The study of protein folding has been greatly advanced in recent years by the development
of fast, time-resolved techniques. These are experimental methods for rapidly triggering the
folding of a sample of unfolded protein, and then observing the resulting dynamics. Fast
techniques in widespread use include neutron scattering , ultrafast mixing of solutions,
photochemical methods, and laser temperature jump spectroscopy. Among the many
scientists who have contributed to the development of these techniques are Jeremy Cook,
Heinrich Roder, Harry Gray, Martin Gruebele, Brian Dyer, William Eaton, Sheena Radford,
Chris Dobson, Sir Alan R. Fersht and Bengt Nolting.

Energy landscape theory of protein folding

The protein folding phenomenon was largely an experimental endeavor until the
formulation of energy landscape theory by Joseph Bryngelson and Peter Wolynes in the late
1980s and early 1990s. This approach introduced the principle of minimal frustration,
which asserts that evolution has selected the amino acid sequences of natural proteins so
that interactions between side chains largely favor the molecule's acquisition of the folded
state. Interactions that do not favor folding are selected against, although some residual
frustration is expected to exist. A consequence of these evolutionarily selected sequences is
that proteins are generally thought to have globally 'Tunneled energy landscapes" (coined
by Jose Onuchic[reference needed]) that are largely directed towards the native state. This
"folding funnel" landscape allows the protein to fold to the native state through any of a
large number of pathways and intermediates, rather than being restricted to a single
mechanism. The theory is supported by both computational simulations of model proteins
and numerous experimental studies, and it has been used to improve methods for protein
structure prediction and design.

Computational prediction of protein tertiary structure

De novo or ab initio techniques for computational protein structure prediction is related to,
but strictly distinct from, studies involving protein folding. Molecular Dynamics (MD) is an
important tool for studying protein folding and dynamics in silico. Because of computational
cost, ab initio MD folding simulations with explicit water are limited to peptides and very
small proteins. MD simulations of larger proteins remain restricted to dynamics of the
experimental structure or its high-temperature unfolding. In order to simulate long time
folding processes (beyond about 1 microsecond), like folding of small-size proteins (about
50 residues) or larger, some approximations or simplifications in protein models need to be
introduced. An approach using reduced protein representation (pseudo-atoms representing

groups of atoms are defined) and statistical potential is not only useful in protein structure

n 71
prediction, but is also capable of reproducing the folding pathways.

Protein folding 181

There are distributed computing projects which use idle CPU time of personal computers to
solve problems such as protein folding or prediction of protein structure. People can run
these programs on their computer or PlayStation 3 to support them. See links below (for
example Folding@Home) to get information about how to participate in these projects.

Experimental techniques of protein structure determination

Folded structures of proteins are routinely determined by X-ray crystallography and NMR.

See also

Anfinsen's dogma

Chevron plot

Denaturation (biochemistry)

Denaturation midpoint

Downhill folding

Equilibrium unfolding

Folding (chemistry)

Folding@Home

Foldit computer game

Levinthal paradox

Protein design

Protein dynamics

Protein structure prediction

Protein structure prediction software

Rosetta@Home

Software for molecular mechanics modeling

References

[1] Alberts, Bruce; Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walters (2002).

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term=mboc4[book]+AND+37

Shape and Structure of Proteins". Molecular Biology of the Cell; Fourth Edition. New York and London: Garland

Science. ISBN 0-8153-3218-1.
[2] Anfinsen C (1972). "The formation and stabilization of protein structure". Biochem.J. 128 (4): 737-49. PMID

4565129.
[3] Jeremy M. Berg, John L. Tymoczko, Lubert Stryer; Web content by Neil D. Clarke (2002).

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term=stryer[book]+AND+2i:

Protein Structure and Function". Biochemistry. San Francisco: W.H. Freeman. ISBN 0-7167-4684-0.
[4] http://folding. Stanford. edu/science.html| "Science of Folding@Home". July 18, 2005. http://folding. Stanford.

edu/science.html. Retrieved on 2007-04-22.
[5] van den Berg B, Wain R, Dobson CM, Ellis RJ (August 2000).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid= 306593| Macromolecular

crowding perturbs protein refolding kinetics: implications for folding inside the cell". EmboJ. 19 (15): 3870-5.

doi: 10. 1093/emboj/19. 15. 3870 (http://dx.doi.org/10.1093/emboj/19.15.3870). PMID 10921869.
[6] Pace C, Shirley B, McNutt M, Gajiwala K (01 Jan 1996). "http://www.fasebj.org/cgi/reprint/10/l/75|Forces

contributing to the conformational stability of proteins". FasebJ. 10 (1): 75-83. PMID 8566551. http://www.

fasebj.org/cgi/reprin t/1 0/1/75.
[7] Rose G, Fleming P, Banavar J, Maritan A (2006). "A backbone-based theory of protein folding". Proc. Natl.

Acad. Sci. U.S.A. 103 (45): 16623-33. doi: 10. 1073/pnas. 0606843103 (http://dx.doi.org/10.1073/pnas.

0606843103). PMID 17075053.
[8] Deechongkit S, Nguyen H, Dawson PE, Gruebele M, Kelly JW (2004). "Context Dependent Contributions of

Backbone H-Bonding to p-Sheet Folding Energetics". Nature 403 (45): 101-5. doi: 10. 1073/pnas. 0606843103

(http://dx.doi.org/10.1073/pnas.0606843103). PMID 17075053.

Protein folding 182

[9] Lee S, Tsai F (2005). "http://www.jbmb. or.kr/fulltext/jbmb/view.php?vol=38&page=259|Molecular chaperones

in protein quality control". J". Biochem. Mol. Biol. 38 (3): 259-65. PMID 15943899. http://www.jbmb.or.kr/

fulltext/jbmb/view.php?vol=38&page=259.
[10] Alexander PA, He Y, Chen Y, Orban J, Bryan PN. (2007).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=l 906725 |The design and

characterization of two proteins with 88% sequence identity but different structure and function". Proc Natl

Acad Sci USA. 104 (29): 11963-8. doi: 10. 1073/pnas. 0700922104 (http://dx.doi.org/10.1073/pnas.

0700922104). PMID 17609385.
[11] Shortle D (01 Jan 1996). "http://www.fasebj.org/cgi/reprint/10/l/27|The denatured state (the other half of the

folding equation) and its role in protein stability". FasebJ. 10 (1): 27-34. PMID 8566543. http://www.fasebj.

org/cgi/reprint/10/1/27.
[12] Kim PS, Baldwin RL (1990). "Intermediates in the folding reactions of small proteins". Annu. Rev. Biochem.

59: 631-60. doi: 10. 1146/annurev.bi.59. 070190. 003215 (http://dx.doi.org/10.1146/annurev.bi.59.070190.

003215). PMID 2197986.
[13] Jackson SE (August 1998). "http://biomednet.com/elecref/13590278003R0081IHow do small single-domain

proteins fold?". Fold Des 3 (4): R81-91. doi: 10.1016/S1359-0278(98)00033-9 (http://dx.doi.org/10.1016/

S1359-0278(98)00033-9). PMID 9710577. http://biomednet.com/elecref/13590278003R0081.
[14] Kubelka J, Hofrichter J, Eaton WA (February 2004). "The protein folding 'speed limit'". Curr. Opin. Struct.

Biol. 14 (1): 76-88. doi: 10.1016/j.sbi.2004.01.013 (http://dx.doi.Org/10.1016/j.sbi.2004.01.013). PMID

15102453.
[15] C. Levinthal (1968). "http://www.biochem.wisc.edu/courses/biochem704/Reading/Levinthall968.pdflAre there

pathways for protein folding?". J". Chim. Phys. 65: 44-5. http://www.biochem.wisc.edu/courses/biochem704/

Reading/Levin thall968.pdf.
[16] Bu Z, Cook J, Callaway DJE (2001). "Dynamic regimes and correlated structural dynamics in native and

denatured alpha-lactalbuminC". J Mol Biol 312 (4): 865-873. doi: 10.1006/jmbi.2001.5006 (http://dx.doi.org/

10.1006/jmbi.2001.5006).
[17] Kmiecik S and Kolinski A (2007). "Characterization of protein-folding pathways by reduced-space modeling".

Proc. Natl. Acad. Sci. U.S.A. 104 (30): 12330-5. doi: 10. 1073/pnas. 0702265104 (http://dx.doi.org/10.1073/

pnas. 0702265104). PMID 17636132.

External links

• Foldlt - Folding Protein Game (http://fold.it/portal/info/science)

• Folding@Home (http://www.stanford.edu/group/pandegroup/folding/about.html)

• Rosetta@Home (http://boinc.bakerlab.org/rosetta)

Protein-protein interaction 183

Protein-protein interaction

Protein-protein interactions involve not only the direct-contact association of protein
molecules but also longer range interactions through the electrolyte, aqueous solution
medium surrounding neighbor hydrated proteins over distances from less than one

nanometer to distances of several tens of nanometers. Furthermore, such protein-protein

rn
interactions are thermodynamically linked functions of dynamically bound ions and water

that exchange rapidly with the surrounding solution by comparison with the molecular

tumbling rate (or correlation times) of the interacting proteins. Protein associations are also

studied from the perspectives of biochemistry, quantum chemistry, molecular dynamics,

signal transduction and other metabolic or genetic/epigenetic networks. Indeed,

protein-protein interactions are at the core of the entire Interactomics system of any living

cell.

The interactions between proteins are important for very numerous— if not all— biological
functions. For example, signals from the exterior of a cell are mediated to the inside of that
cell by protein-protein interactions of the signaling molecules. This process, called signal
transduction, plays a fundamental role in many biological processes and in many diseases
(e.g. cancers). Proteins might interact for a long time to form part of a protein complex, a
protein may be carrying another protein (for example, from cytoplasm to nucleus or vice
versa in the case of the nuclear pore importins), or a protein may interact briefly with
another protein just to modify it (for example, a protein kinase will add a phosphate to a
target protein). This modification of proteins can itself change protein-protein interactions.
For example, some proteins with SH2 domains only bind to other proteins when they are
phosphorylated on the amino acid tyrosine while bromodomains specifically recognise
acetylated lysines. In conclusion, protein-protein interactions are of central importance for
virtually every process in a living cell. Information about these interactions improves our
understanding of diseases and can provide the basis for new therapeutic approaches.

Methods to investigate protein-protein interactions

Biochemical methods

As protein-protein interactions are so important there are a multitude of methods to detect
them. Each of the approaches has its own strengths and weaknesses, especially with regard
to the sensitivity and specificity of the method. A high sensitivity means that many of the
interactions that occur in reality are detected by the screen. A high specificity indicates
that most of the interactions detected by the screen are also occurring in reality.

• Co-immunoprecipitation is considered to be the gold standard assay for protein-protein
interactions, especially when it is performed with endogenous (not overexpressed and
not tagged) proteins. The protein of interest is isolated with a specific antibody.
Interaction partners which stick to this protein are subsequently identified by western
blotting. Interactions detected by this approach are considered to be real. However, this
method can only verify interactions between suspected interaction partners. Thus, it is
not a screening approach. A note of caution also is that immunoprecipitation experiments
reveal direct and indirect interactions. Thus, positive results may indicate that two
proteins interact directly or may interact via a bridging protein.

Protein-protein interaction 1 84

• Bimolecular Fluorescence Complementation (BiFC) is a new technique in observing the
interactions of proteins. Combining with other new techniques, this method can be used
to screen protein-protein interactions and their modulators .

• Affinity electrophoresis as used for estimation of binding constants, as for instance in
lectin affinity electrophoresis or characterization of molecules with specific features like
glycan content or ligand binding.

• Pull-down assays are a common variation of immunoprecipitation and
immunoelectrophoresis and are used identically, although this approach is more
amenable to an initial screen for interacting proteins.

• Label transfer can be used for screening or confirmation of protein interactions and can
provide information about the interface where the interaction takes place. Label transfer
can also detect weak or transient interactions that are difficult to capture using other in
vitro detection strategies. In a label transfer reaction, a known protein is tagged with a
detectable label. The label is then passed to an interacting protein, which can then be
identified by the presence of the label.

• The yeast two-hybrid screen investigates the interaction between artificial fusion
proteins inside the nucleus of yeast. This approach can identify binding partners of a
protein in an unbiased manner. However, the method has a notorious high false-positive
rate which makes it necessary to verify the identified interactions by
co-immunoprecipitation.

• In-vivo crosslinking of protein complexes using photo-reactive amino acid analogs was
introduced in 2005 by researchers from the Max Planck Institute In this method, cells
are grown with photoreactive diazirine analogs to leucine and methionine, which are
incorporated into proteins. Upon exposure to ultraviolet light, the diazirines are activated
and bind to interacting proteins that are within a few angstroms of the photo-reactive
amino acid analog.

• Tandem affinity purification (TAP) method allows high throughput identification of
protein interactions. In contrast to Y2H approach accuracy of the method can be
compared to those of small-scale experiments (Collins et al., 2007) and the interactions
are detected within the correct cellular environment as by co-immunoprecipitation.
However, the TAP tag method requires two successive steps of protein purification and
consequently it can not readily detect transient protein-protein interactions. Recent
genome-wide TAP experiments were performed by Krogan et al., 2006 and Gavin et al.,
2006 providing updated protein interaction data for yeast organism.

• Chemical crosslinking is often used to "fix" protein interactions in place before trying to
isolate/identify interacting proteins. Common crosslinkers for this application include the
non-cleavable NHS-ester crosslinker, bz's-sulfosuccinimidyl suberate (BS3); a cleavable
version of BS3, dithiobis(sulfosuccinimidyl propionate) (DTSSP); and the imidoester
crosslinker dimethyl dithiobispropionimidate (DTBP) that is popular for fixing
interactions in ChIP assays.

• Chemical crosslinking followed by high mass MALDI mass spectrometry can be used to
analyze intact protein interactions in place before trying to isolate/identify interacting
proteins. This method detects interactions among non-tagged proteins and is available
from CovalX.

• SPINE (Strep-protein interaction experiment) uses a combination of reversible
crosslinking with formaldehyde and an incorporation of an affinity tag to detect
interaction partners in vivo.

Protein-protein interaction 185

• Quantitative immunoprecipitation combined with knock-down (QUICK) relies on
co-immunoprecipitation, quantitative mass spectrometry (SILAC) and RNA interference
(RNAi). This method detects interactions among endogenous non-tagged proteins .
Thus, it has the same high confidence as co-immunoprecipitation. However, this method
also depends on the availability of suitable antibodies.

Physical/Biophysical and Theoretical methods

• Dual Polarisation Interferometry (DPI) can be used to measure protein-protein
interactions. DPI provides real-time, high-resolution measurements of molecular size,
density and mass. While tagging is not necessary, one of the protein species must be
immobilized on the surface of a waveguide.

• Static Light scattering (SLS) measures changes in the Rayleigh scattering of protein
complexes in solution and can non-destructively characterize both weak and strong
interactions without tagging or immobilization of the protein. The measurement consists
of mixing a series of aliquots of different concentrations or compositions with the anylate,
measuring the effect of the changes in light scattering as a result of the interaction, and
fitting the correlated light scattering changes with concentration to a model. Weak,
non-specific interactions are typically characterized via the second virial coefficient. This
type of analysis can determine the equilibrium association constant for associated
complexes. . Additional light scattering methods for protein activity determination
were previously developed by Timasheff. More recent Dynamic Light scattering (DLS)
methods for proteins were reported by H. Chou that are also applicable at high protein
concentrations and in protein gels; DLS may thus also be applicable for in vivo
cytoplasmic observations of various protein-protein interactions.

• Surface plasmon resonance can be used to measure protein-protein interaction.

• With Fluorescence correlation spectroscopy, one protein is labeled with a fluorescent dye
and the other is left unlabeled. The two proteins are then mixed and the data outputs the
fraction of the labeled protein that is unbound and bound to the other protein, allowing
you to get a measure of K and binding affinity. You can also take time-course
measurements to characterize binding kinetics. FCS also tells you the size of the formed
complexes so you can measure the stoichiometry of binding. A more powerful methods is
[[fluorescence cross-correlation spectroscopy (FCCS) that employs double labeling
techniques and cross-correlation resulting in vastly improved signal-to-noise ratios over
FCS. Furthermore, the two-photon and three-photon excitation practically eliminates
photobleaching effects and provide ultra-fast recording of FCCS or FCS data.

• Fluorescence resonance energy transfer (FRET) is a common technique when observing
the interactions of only two different proteins .

• Protein activity determination by NMR multi-nuclear relaxation measurements, or 2D-FT
NMR spectroscopy in solutions, combined with nonlinear regression analysis of NMR
relaxation or 2D-FT spectroscopy data sets. Whereas the concept of water activity is
widely known and utilized in the applied biosciences, its complement-the protein activity
which quantitates protein-protein interactions- is much less familiar to bioscientists as it
is more difficult to determine in dilute solutions of proteins; protein activity is also much
harder to determine for concentrated protein solutions when protein aggregation, not
merely transient protein association, is often the dominant process .

• Theoretical modeling of protein-protein interactions involves a detailed physical
chemistry/thermodynamic understanding of several effects involved, such as

Protein-protein interaction 186

intermolecular forces, ion-binding, proton fluctuations and proton exchange. The theory
of thermodynamically linked functions is one such example in which ion-binding and
protein-protein interactions are treated as linked processes; this treatment is especially
important for proteins that have enzymatic activity which depends on cofactor ions
dynamically bound at the enzyme active site, as for example, in the case of
oxygen-evolving enzyme system (OES) in photosythetic biosystems where the oxygen
molecule binding is linked to the chloride anion binding as well as the linked state
transition of the manganese ions present at the active site in Photosystem II(PSII).
Another example of thermodynamically linked functions of ions and protein activity is
that of divalent calcium and magnesium cations to myosin in mechanical energy
transduction in muscle. Last-but-not least, chloride ion and oxygen binding to hemoglobin
(from several mammalian sources, including human) is a very well-known example of
such thermodynamically linked functions for which a detailed and precise theory has
been already developed.

• Molecular dynamics (MD) computations of protein-protein interactions.

• Protein-protein docking, the prediction of protein-protein interactions based only on the
three-dimensional protein structures from X-ray diffraction of protein crystals might not
be satisfactory. [9] [10]

Network visualization of protein-protein interactions

Visualization of protein-protein interaction networks is a popular application of scientific
visualization techniques. Although protein interaction diagrams are common in textbooks,
diagrams of whole cell protein interaction networks were not as common since the level of
complexity made them difficult to generate. One example of a manually produced molecular
interaction map is Kurt Kohn's 1999 map of cell cycle control. Drawing on Kohn's map,
in 2000 Schwikowski, Uetz, and Fields published a paper on protein-protein interactions in
yeast, linking together 1,548 interacting proteins determined by two-hybrid testing. They
used a force-directed (Sugiyama) graph drawing algorithm to automatically generate an
image of their network. [12] [13] [14] .

An experimental view of Kurt Kohn's 1999 map gmap . Image was merged via gimp
2.2.17 and then uploaded to maplib.net

See also

Interactomics

Signal transduction

Biophysical techniques

Biochemistry methods

Genomics

Complex systems biology

Complex systems

Immunoprecipitation

Protein-protein interaction prediction

Protein-protein interaction screening

BioGRID, a public repository for protein and genetic interactions

Database of Interacting Proteins (DIP)

NCIBI National Center for Integrative Biomedical Informatics

Protein-protein interaction 187

• Biotechnology

• Protein nuclear magnetic resonance spectroscopy

• 2D-FT NMRI and Spectroscopy

• Fluorescence correlation spectroscopy

• Fluorescence cross-correlation spectroscopy

• Light scattering

• ConsensusPathDB

References

[I] Kinetic Linked-Function Analysis of the Multiligand Interactions on Mg2+-Activated Yeast Pyruvate Kinase.
Thomas J. Bollenbach and Thomas Nowak., Biochemistry, 2001, 40 (43), pp. 13097-13106

[2] Lu JP, Beatty LK, Pinthus JH. (2008). "Dual expression recombinase based (DERB) single vector system for

high throughput screening and verification of protein interactions in living cells.". Nature Precedings

<http://hdl.handle.net/10101/npre.2008. 1550. 2>.
[3] Suchanek, M., Radzikowska, A., and Thiele, C. (2005). "Photo-leucine and photo-methionine allow

identification of protein-protein interactions in living cells". Nature Methods 2: 261-268. doi:

10.1038/nmeth752 (http://dx.doi.org/10.1038/nmeth752). PMID 15782218.
[4] Herzberg C, Weidinger LA., Dorrbecker B., Hiibner S., Stiilke J. and Commichau FM. (2007). "SPINE: A

method for the rapid detection and analysis of protein-protein interactions in vivo". Proteomics 7(22):

4032-4035. doi: 10.1002/pmic.200700491 (http://dx.doi.org/10.1002/pmic.200700491). PMID 17994626.
[5] Selbach, M., Mann, M. (2006). "Protein interaction screening by guantitative immunoprecipitation combined

with knockdown (QUICK)". Nature Methods 3: 981-983. doi: 10.1038/nmeth972 (http://dx.doi.org/10.1038/

nmeth972). PMID 17072306.
[6] Arun K. Attri and Allen P. Minton (2005). "Composition gradient static light scattering: A new technigue for

rapid detection and guantitative characterization of reversible macromolecular hetero-associations in solution".

Analytical Biochemistry 346: 132-138. doi: 10.1016/j.ab.2005.08.013 (http://dx.doi.Org/10.1016/j.ab. 2005.

08.013). PMID 16188220.
[7] GadellaTWJr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN 978-0-08-054958-3. (2008) 560 pages.
[8] #Baianu, I.C.; Kumosinski, Thomas (August 1993). "NMR Principles and Applications to Protein Structure,

Activity and Hydration.,". Ch.9 in Physical Chemistry of Food Processes: Advanced Technigues and

Applications. (New York: Van Nostrand-Reinhold) 2: 338-420. ISBN 0-442-00582-2.
[9] Bonvin AM (2006). "Flexible protein-protein docking". Current Opinion in Structural Biology 16: 194-200. doi:

10.1016/j.sbi.2006.02.002 (http://dx.doi.Org/10.1016/j.sbi.2006.02.002). PMID 16488145.
[10] GrayJJ (2006). "High-resolution protein-protein docking". Current Opinion in Structural Biology 16: 183-193.

doi: 10.1016/j.sbi.2006.03.003 (http://dx.doi.Org/10.1016/j.sbi.2006.03.003). PMID 16546374.

[II] KurtW. Kohn(1999).
"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid= 1043602 3 |Molecular
Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems". Molecular Biology of the Cell
10 (8): 2703-2734. PMID 10436023. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&
pubmedid=10436023.

[12] Benno Schwikowskil, Peter Uetz, and Stanley Fields (2000).

"http://igtmvl.fzk.de/www/itg/uetz/publications/Schwikowski2000.pdflA network of protein -protein
interactions in yeast". Nature Biotechnology 18: 1257-1261. doi: 10.1038/82360 (http://dx.doi.org/10.1038/
82360). PMID 11101803. http://igtmvl.fzk.de/www/itg/uetz/publications/Schwikowski2000.pdf.

[13] Rigaut G, Shevchenko A, Rutz B, Wilm M, Mann M, Seraphin B (1999) A generic protein purification method
for protein complex characterization and proteome exploration. Nat Biotechnol. 17:1030-2.

[14] Prieto C, De Las Rivas J (2006). APID: Agile Protein Interaction DataAnalyzer. Nucleic Acids Res.
34:W298-302.

[15] http://www.maplib. net/map. php?id=1700&lat=-52.67138590320257&lng=34.3817138671875&z=9

Protein-protein interaction 188

Further reading

1. Gadella TW Jr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN
978-0-08-054958-3. (2008) 560 pages

2. Langel FD, et al., Multiple protein domains mediate interaction between BcllO and
Maltl,/. Biol. Chem., (2008) 283(47):32419-31

3. Clayton AH. , The polarized AB plot for the frequency-domain analysis and
representation of fluorophore rotation and resonance energy homotransfer. J Microscopy.
(2008) 232(2):306-12

4. Clayton AH, et al.. Predominance of activated EGFR higher-order oligomers on the cell
surface. Growth Factors (2008) 20:1

5. Plowman et al., Electrostatic Interactions Positively Regulate K-Ras Nanocluster
Formation and Function. Molecular and Cellular Biology (2008) 4377-4385

6. Belanis L, et al., Galectin-1 Is a Novel Structural Component and a Major Regulator of
H-Ras Nanoclusters. Molecular Biology of the Cell (2008) 19:1404-1414

7. Van Manen HJ, Refractive index sensing of green fluorescent proteins in living cells
using fluorescence lifetime imaging microscopy. Biophys J. (2008) 94(8):L67-9

8. Van der Krogt GNM, et al., A Comparison of Donor-Acceptor Pairs for Genetically
Encoded FRET Sensors: Application to the Epac cAMP Sensor as an Example, PLoS ONE,
(2008) 3(4):el916

9. Dai X, et al.. Fluorescence intensity and lifetime imaging of free and
micellar-encapsulated doxorubicin in living cells. Nanomedicine. (2008) 4(l):49-56.

10. Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by
fluorescence correlation spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.

1 1 . Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical
Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds,
Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and
Analysis., D. Luthria, Editor pp. 241-273, AOCS Press., Champaign, IL

12. Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT)
Spectroscopy. Nobel Lecture, on December 9, 1992.

13. Baianu, I.C; Kumosinski, Thomas (August 1993). "NMR Principles and Applications to
Protein Structure, Activity and Hydration.,". Ch.9 in Physical Chemistry of Food
Processes: Advanced Techniques and Applications. (New York: Van Nostrand-Reinhold)
2: 338-420. ISBN 0-442-00582-2.

14. Kurt Wiithrich in 1982-1986 : 2D-FT NMR of solutions (http://en.wikipedia.org/wiki/
Nuclear_magnetic_resonance#Nuclear_spin_and_magnets)

15. Charles P. Slichter.1996. Principles of Magnetic Resonance., Springer: Berlin and New
York, Third Edition., 651pp. ISBN 0-387-50157-6.

16. Kurt Wiithrich. Protein structure determination in solution by NMR spectroscopy . J
Biol Chem. 1990, December 25;265(36):22059-62.

Protein-protein interaction 189

External links

• National Center for Integrative Biomedical Informatics (NCIBI) (http://portal.ncibi.org/
gateway/)

• Proteins and Enzymes (http://www.dmoz.org/Science/Biology/
BiochemistryandMolecularBiology/Biomolecules/ProteinsandEnzymes/) at the
Open Directory Project

• FLIM Applications (http://www.nikoninstruments.com/infocenter.php?n=FLIM) FLIM
is also often used in microspectroscopic/ chemical imaging, or microscopic, studies to
monitor spatial and temporal protein-protein interactions, properties of membranes and
interactions with nucleic acids in living cells.

• Arabidopsis thaliana protein interaction network (http://bioinfo.esalq.usp.br/atpin)

DNA Dynamics

DNA Molecular dynamics modeling involves simulations of DNA molecular geometry
and topology changes with time as a result of both intra- and inter- molecular interactions
of DNA. Whereas molecular models of Deoxyribonucleic acid (DNA) molecules such as
closely packed spheres (CPK models) made of plastic or metal wires for 'skeletal models'
are useful representations of static DNA structures, their usefulness is very limited for
representing complex DNA dynamics. Computer molecular modeling allows both
animations and molecular dynamics simulations that are very important for understanding
how DNA functions in vivo.

An old standing dynamic problem is how DNA "self-replication" takes place in living cells
that should involve transient uncoiling of supercoiled DNA fibers. Although DNA consists of
relatively rigid, very large elongated biopolymer molecules called "fibers" or chains its
molecular structure in vivo undergoes dynamic configuration changes that involve
dynamically attached water molecules, ions or proteins/enzymes. Supercoiling, packing
with histones in chromosome structures, and other such supramolecular aspects also
involve in vivo DNA topology which is even more complex than DNA molecular geometry,
thus turning molecular modeling of DNA dynamics into a series of challenging problems for
biophysical chemists, molecular biologists and biotechnologists. Thus, DNA exists in
multiple stable geometries (called conformational isomerism) and has a rather large
number of configurational, quantum states which are close to each other in energy on the
potential energy surface of the DNA molecule.

Such varying molecular geometries can also be computed, at least in principle, by
employing ab initio quantum chemistry methods that can attain high accuracy for small
molecules, although claims that acceptable accuracy can be also achieved for
polynucleotides, as well as DNA conformations, were recently made on the basis of VCD
spectral data. Such quantum geometries define an important class of ab initio molecular
models of DNA whose exploration has barely started especially in connection with results
obtained by VCD in solutions. More detailed comparisons with such ab initio quantum
computations are in principle obtainable through 2D-FT NMR spectroscopy and relaxation
studies of polynucleotide solutions or specifically labeled DNA, as for example with
deuterium labels.

DNA Dynamics 190

Importance of DNA molecular structure and dynamics
modeling for Genomics and beyond

From the very early stages of structural studies of DNA by X-ray diffraction and
biochemical means, molecular models such as the Watson-Crick double-helix model were
successfully employed to solve the 'puzzle' of DNA structure, and also find how the latter
relates to its key functions in living cells. The first high quality X-ray diffraction patterns of
A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953 . The first
reports of a double-helix molecular model of B-DNA structure were made by Watson and
Crick in 1953 [2] [3] . Then Maurice F. Wilkins, A. Stokes and H.R. Wilson, reported the first
X-ray patterns of in vivo B-DNA in partially oriented salmon sperm heads . The

development of the first correct double-helix molecular model of DNA by Crick and Watson
may not have been possible without the biochemical evidence for the nucleotide
base-pairing ([A— T]; [C— G]), or Chargaff's rules [5] [6] [7] [8] [9] [10] . Although such initial
studies of DNA structures with the help of molecular models were essentially static, their
consequences for explaining the in vivo functions of DNA were significant in the areas of
protein biosynthesis and the quasi-universality of the genetic code. Epigenetic
transformation studies of DNA in vivo were however much slower to develop in spite of
their importance for embryology, morphogenesis and cancer research. Such chemical
dynamics and biochemical reactions of DNA are much more complex than the molecular
dynamics of DNA physical interactions with water, ions and proteins/enzymes in living cells.

Animated DNA molecular models and hydrogen-bonding

DNA. The last two DNA molecular models in this series depict quadruplex DNA that

rm ri2i
may be involved in certain cancers . The first CPK model in the second row is a

molecular model of hydrogen bonds between water molecules in ice that are broadly similar

to those found in DNA; the hydrogen bonding dynamics and proton exchange is however

very different by many orders of magnitude between the two systems of fully hydrated DNA

and water molecules in ice. Thus, the DNA dynamics is complex, involving nanosecond and

several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time

scale, and that of proton exchange in ice is on the millisecond time scale; the proton

exchange rates in DNA and attached proteins may vary from picosecond to nanosecond,

minutes or years, depending on the exact locations of the exchanged protons in the large

biopolymers. The simple harmonic oscillator 'vibration' in the third, animated image of the

next gallery is only an oversimplified dynamic representation of the longitudinal vibrations

of the DNA intertwined helices which were found to be anharmonic rather than harmonic as

often assumed in quantum dynamic simulations of DNA.

DNA Dynamics

191

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DNA Dynamics

192

Human Genomics and Biotechnology Applications of DNA
Molecular Modeling

The following two galleries of images illustrate various uses of DNA molecular modeling in
Genomics and Biotechnology research applications from DNA repair to PCR and DNA
nanostructures; each slide contains its own explanation and/or details. The first slide
presents an overview of DNA applications, including DNA molecular models, with emphasis
on Genomics and Biotechnology.

Applications of DNA molecular dynamics computations

• First row images present a DNA biochip and DNA nanostructures designed for DNA
computing and other dynamic applications of DNA nanotechnology; last image in this row
is of DNA arrays that display a representation of the Sierpinski gasket on their surfaces.

• Second row. the first two images show computer molecular models of RNA polymerase,
followed by that of an E. coli, bacterial DNA primase template suggesting very complex
dynamics at the interfaces between the enzymes and the DNA template; the fourth image
illustrates in a computed molecular model the mutagenic, chemical interaction of a
potent carcinogen molecule with DNA, and the last image shows the different
interactions of specific fluorescence labels with DNA in human and orangoutan
chromosomes.

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DNA Dynamics

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Image Gallery: DNA Applications and Technologies at various scales
in Biotechnology and Genomics research

The first figure is an actual electron micrograph of a DNA fiber bundle, presumably of a
single plasmid, bacterial DNA loop.

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DNA Dynamics

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Databases for Genomics, DNA Dynamics and Sequencing

Genomic and structural databases

• CBS Genome Atlas Database — contains examples of base skews.

• The Z curve database of genomes — a 3-dimensional visualization and analysis tool of
genomes [59][14] .

• DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids
molecular structure models in PDB and CIF formats

DNA Dynamics

195

Mass spectrometry— Maldi informatics

Data acquisition

I List of peak
I masses

Peak detection

_ 5 J List of peak
^n intensities

Genotype,
mutations, etc.

DNA Dynamics Data from Spectroscopy

• FT-NMR [15] [16]

• NMR Atlas-database [29]

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data

[30]

• NMR constraints files for NAs in PDB format [31]
NMR microscopy'- ^
Vibrational circular dichroism (VCD)
Microwave spectroscopy
FT-IR

FT-NIR [18] [19] [20]

Spectral Hyperspectral, and Chemical imaging) [21] [22] [23] [24] [25] [26] [27] .
Raman spectroscopy/microscopy and CARS

Fluorescence correlation spectroscopy' 301 [31] [32] [33] [34] [35] [36] [37] , Fluorescence
cross-correlation spectroscopy and FRET

Confocal microscopy

[41]

DNA Dynamics

196

Gallery: CARS (Raman spectroscopy), Fluorescence confocal
microscopy, and Hyperspectral imaging

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DNA Dynamics

197

X-ray microscopy

• Application of X-ray microscopy in the analysis of living hydrated cells

[18]

Atomic Force Microscopy (AFM)

Two-dimensional DNA junction arrays have been visualized by Atomic Force Microscopy
(AFM) [ ] . Other imaging resources for AFM/Scanning probe microscopy(SPM) can be
freely accessed at:

• How SPM Works [25]

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [26]

Gallery of AFM Images of DNA Nanostructures

Notes

[1] Franklin, R.E. and Gosling, R.G. recd.6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium

Thymonucleate Fibres I. The Influence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium

Thymonucleate Fibres II. The Cylindrically Symmetrical Patterson Function.
[2] Watson, J.D; Crick F.H.C. 1953a. Molecular Structure of Nucleic Acids- A Structure for Deoxyribose Nucleic

Acid., Nature 171(4356):737-738.
[3] Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Quantitative Biology

18:123-131.
[4] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R (1953).

"http://www.nature.com/nature/dna50/wilkins.pdflMolecular Structure of Deoxypentose Nucleic Acids" (PDF).

Nature 111. 738-740. doi: 10.1038/171738a0 (http://dx.doi.org/10.1038/171738a0). PMID 13054693. http:/

/www. nature.com/nature/dna50/wilkins.pdf.
[5] Elson D, Chargaff E (1952). "On the deoxyribonucleic acid content of sea urchin gametes". Experientia 8 (4):

143-145.
[6] Chargaff E, Lipshitz R, Green C (1952). "Composition of the deoxypentose nucleic acids of four genera of

sea-urchin". J Biol Chem 195 (1): 155-160. PMID 14938364.
[7] Chargaff E, Lipshitz R, Green C, Hodes ME (1951). "The composition of the deoxyribonucleic acid of salmon

sperm". J Biol Chem 192 (1): 223-230. PMID 14917668.

DNA Dynamics 198

[8] Chargaff E (1951). "Some recent studies on the composition and structure of nucleic acids". J" Cell Physiol

Suppl 38 (Suppl).
[9] Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E (1950). "The separation and estimation of

ribonucleotides in minute guantities". J Biol Chem 186 (1): 37-50. PMID 14778802.
[10] Chargaff E (1950). "Chemical specificity of nucleic acids and mechanism of their enzymatic degradation".

Experientia 6 (6): 201-209.
[11] http ://www. phy. cam. ac. uk/research/bss/molbiophysics . php
[12] http://planetphysics.org/encyclopedia/TheoreticalBiophysics.html
[13] Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic results

and DNA seguence data". Bioinformatics 20: 3682-3686.
[14] Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome seguences".

Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041
[15] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants
[16] (http ://www. spectroscopynow. com/FCKeditor/UserFiles/File/specNOW/HTML files/

General_Karplus_Calculator.htm) Another Javascript-like NMR coupling constant to dihedral
[17] Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.
[18] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.e. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[19] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

g-bio/0407006 (July 2004) (http://arxiv.org/abs/g-bio/0407006)
[20] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.
[21] http://www.imaging.net/chemical-imaging/Chemical imaging
[22] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee

and L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical

Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.
[23] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy.,

Microchimica Acta, 104, (1-6) January 1991, doi: 10.1007/BF01245536
[24] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.e. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[25] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

g-bio/0407006 (July 2004) (http://arxiv.org/abs/g-bio/0407006)
[26] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical

Industry, G.I.T. Laboratory Journal Europe, No. 1-2, 2007.
[27] Applications of Novel Technigues to Health Foods, Medical and Agricultural Biotechnology. (June 2004)., I. C.

Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin g-bio/0406047 (http://arxiv.org/abs/g-bio/0406047)
[28] Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/ImagingMicroscopy04.pdf)
[29] C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for

Biology and Medicine., doi:10.1146/annurev.anchem. 1.031207. 112754 Annual Review of Analytical Chemistry,

1: 883-909.
[30] Eigen, M., Rigler, M. Sorting single molecules: application to diagnostics and evolutionary

biotechnology, (1994) Proc. Natl. Acad. Sci. USA, 91,5740-5747.
[31] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in

biotechnology,(1995) J. Biotechnol., 41,177-186.
[32] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation

spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.
[33] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al.,

g-bio/0407006 (July 2004) (http://arxiv.org/abs/g-bio/0407006)
[34] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid seguence-based

amplification combined with fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.
[35] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in

giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.

DNA Dynamics 199

[36] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by

fluorescence correlation spectroscopy with one- and two-photon excitation. Biophysical Journal,

77(10):2251-2265.
[37] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.e. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[38] FRET description (http://dwb.unl.edu/Teacher/NSF/C08/C08Links/pps99.cryst.bbk.ac.uk/projects/

gmocz/fret.htm)
[39] doi:10.1016/S0959-440X(00)00190-l (http://dx.doi.org/10. 1016/S0959-440X(00)00190-l)Recent

advances in FRET: distance determination in protein-DNA complexes. Current Opinion in Structural Biology

2001, 11(2), 201-207
[40] http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction
[41] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary

biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.
[42] Mao, Chengde; Sun, Weigiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA

Holliday Junction Arrays Visualized by Atomic Force Microscopy". Journal of the American Chemical Society

121 (23): 5437-5443. doi: 10.1021/ja9900398 (http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863

(http://worldcat.org/issn/0002-7863).

References

Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and

Sons, Ltd., vols. 1 and 2., 1966., 2024 pages.

F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen

(1824), article 14.

Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II. , San Franscisco:

W.H. Freeman and Co. 1980. 1,800 pages.

Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics

and evolutionary biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.

Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology,

Marcel-Dekker, New York, NY.

Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by

fluorescence correlation spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.

Applications of Novel Techniques to Health Foods, Medical and Agricultural

Biotechnology. (June 2004) I. C. Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin.,

q-bio/0406047.

Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical

Imaging and Fluorescence Microspectroscopy.2004. I. C. Baianu, D. Costescu, N. E.

Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004).

Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley

& Sons, Inc., 1995, ISBN 0-471-58651-X., 1361 pages.

Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge

University Press. ISBN 0-521-48391-3.

Watson, James D. and Francis H.C. Crick. A structure for Deoxyribose Nucleic Acid

(http://www.nature.com/nature/dna50/watsoncrick.pdf) (PDF). Nature 111, 737-738,

25 April 1953.

Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A.

Benjamin, Inc. 1965., 494 pages.

Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science,

Inc. 2000.

DNA Dynamics 200

• Herbert R. Wilson, FRS. Diffraction of X-rays by proteins. Nucleic Acids and Viruses.,
London: Edward Arnold (Publishers) Ltd. 1966.

• Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane, Chicester,
Toronto, Singapore: J. Wiley & Sons. 1986., 292 pages.

oxf ordj ournals . org/cgi/content/abstract/ 1/4/295)

• Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun
(November 2003).

DNA Dynamics 201

See also

DNA

Molecular modeling of DNA

Genomics

Signal transduction

Transcriptomics

Interactomics

Biotechnology

Molecular graphics

Quantum computing

MAYA-II

DNA computing

DNA structure

Molecular structure

Molecular dynamics

Molecular topology

DNA topology

DNA, the Genome and Interactome

Molecular structure

Molecular geometry fluctuations

Molecular interactions

Molecular topology

Hydrogen bonding

Hydrophobic interactions

DNA dynamics and conformations

DNA Conformational isomerism

2D-FT NMRI and Spectroscopy

Paracrystalline lattices/Paracrystals

NMR Spectroscopy

VCD or Vibrational circular dichroism

Microwave spectroscopy

Two-dimensional IR spectroscopy

FRET and FCS- Fluorescence correlation spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS)

Spectral imaging

Hyperspectral imaging

Chemical imaging

NMR microscopy

X-ray scattering

Neutron scattering

Crystallography

Crystal lattices

Molecular geometry

Nanostructure

DNA nanotechnology

Imaging

Sirius visualization software

DNA Dynamics 202

Atomic force microscopy

X-ray microscopy

Liquid crystals

Glasses

QMC@Home

Sir Lawrence Bragg, FRS

Sir John Randall

Francis Crick

Manfred Eigen

Felix Bloch

Paul Lauterbur

Maurice Wilkins

Herbert Wilson, FRS

Alex Stokes

External links

• DNAlive: a web interface to compute DNA physical properties (http://mmb.pcb.ub.es/
DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and
DNA dynamics.

• Application of X-ray microscopy in analysis of living hydrated cells (http://www.ncbi.
nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&
list_uids=12379938)

• DiProDB: Dinucleotide Property Database (http://diprodb.fli-leibniz.de). The database
is designed to collect and analyse thermodynamic, structural and other dinucleotide
properties.

• DNA the Double Helix Game (http://nobelprize.org/educational_games/medicine/
dnadoublehelix/) From the official Nobel Prize web site

• MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. wesleyan.edu:8080/
MDDNA/)

• Double Helix 1953-2003 (http://www.ncbe.reading.ac.uk/DNA50/) National Centre
for Biotechnology Education

• DNA under electron microscope (http://www.fidelitysystems.com/Unlinked_DNA.
html)

• Further details of mathematical and molecular analysis of DNA structure based on X-ray
data (http://planetphysics.org/encyclopedia/
BesselFunctionsApplicationsToDiffractionByHelicalStructures.html)

• Bessel functions corresponding to Fourier transforms of atomic or molecular helices.
(http://planetphysics.org/?op=getobj&from=objects&
name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures)

• Characterization in nanotechnology some pdfs (http://nanocharacterization.sitesled.
com/)

• An overview of STM/AFM/SNOM principles with educative videos (http://www.ntmdt.
ru/SPM-Techniques/Principles/)

• SPM Image Gallery - AFM STM SEM MFM NSOM and More (http://www.rhk-tech.com/
results/showcase. php)

• How SPM Works (http://www.parkafm.com/New_html/resources/01general.php)

DNA Dynamics 203

• U.S. National DNA Day (http://www.genome.gov/10506367) — watch videos and
participate in real-time discussions with scientists.

• The Secret Life of DNA - DNA Music compositions (http://www.tjmitchell.com/stuart/
dna.html)

• Ascalaph DNA (http://www.agilemolecule.com/Ascalaph/Ascalaph_DNA.html) —
Commercial software for DNA modeling

DNA nanotechnology

204

DNA nanotechnology

Part of a series of articles on

Molecular self-assembly

Self-assembled monolayer

Supramolecular assembly

DNA nanotechnology

See also

• Mechanical properties of DNA

External links

Chengde Mao page at Purdue University [19]

John Reif lab at Duke University [20]

Nadrian Seeman lab at NYU [21]

William M. Shih lab at Harvard Medical School [22]

Andrew Turberfield lab at Oxford University [23]

Erik Winfree lab at Caltech [24]

Hao Yan lab at Arizona State University [25]

Bernard Yurke formerly at Bell Labs [26] now at Boise State University [27]

Thorn LaBean at Duke University [28]

Software for 3D DNA design, modeling and/or simulation:

• Ascalaph Designer [ ]

• caDNAno [30]

• GIDEON [31]

r^2i

• NanoEngineer-1

International Society for Nanoscale Science, Computation and Engineering [33]

DNA nanotechnology 209

References

Note: Click on the doi to access the text of the referenced article.

[1] Created from PDB 1M6G (http://www.rcsb. org/pdb/explore/explore.do?structureId=lM6G)
[2] http://dx.doi.org/10.1371/journal.pbio.0020431

• Seeman, Nadrian C. (1 November 1999). "DNA Engineering and its Application to Nanotechnology". Trends
in Biotechnology 17 (11): 437-443. doi: 10.1016/S0167-7799(99)01360-8 (http://dx.doi.org/10.1016/
S0167-7799(99)01360-8). ISSN 0167-7799 (http://worldcat.org/issn/0167-7799).

• Seeman, Nadrian C. (January 2001). "DNA Nicks and Nodes and Nanotechnology". Nano Letters 1 (1):
22-26. doi: 10. 1021/nl000182v (http://dx.doi.org/10.1021/nl000182v). ISSN 1530-6984 (http://worldcat.
org/issn/1 530-6984).

• Mao, Chengde (December 2004). "The Emergence of Complexity: Lessons from DNA". PLoS Biology 2 (12):
2036-2038. doi: 10. 1371/journal.pbio. 0020431 (http://dx.doi.org/10.1371/journal.pbio.0020431). ISSN
1544-9173 (http://worldcat.org/issn/1544-9173).

• Kumara, Mudalige T. (July 2008). "Assembly pathway analysis of DNA nanostructures and the construction of
parallel motifs". Nano Letters 8 (7): 1971-1977. doi: 10. 1021/nl800907y (http://dx.doi.org/10.1021/
nl800907y). ISSN .

• Winfree, Erik; Liu, Furong; Wenzler, Lisa A. & Seeman, Nadrian C. (6 August 1998). "Design and
self-assembly of two-dimensional DNA crystals". Nature 394: 529-544. doi: 10.1038/28998 (http://dx.doi.
org/10.1038/28998). ISSN 0028-0836 (http://worldcat.org/issn/0028-0836).

• Liu, Furong; Sha, Ruojie & Seeman, Nadrian C. (10 February 1999). "Modifying the Surface Features of
Two-Dimensional DNA Crystals". Journal of the American Chemical Society 111 (5): 917-922. doi:
10.1021/ja982824a (http://dx.doi.org/10.1021/ja982824a). ISSN 0002-7863 (http://worldcat.org/issn/
0002-7863).

• Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, Deborah Kuchnir &
Winfree, Erik (22 December 2004). "Design and Characterization of Programmable DNA Nanotubes". Journal
of the American Chemical Society 126 (50): 16344-16352. doi: 10.1021/ja0443191 (http://dx.doi.org/10.
1021/ja0443191). ISSN 0002-7863 (http://worldcat.org/issn/0002-7863).

• Mao, Chengde; Sun, Weigiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA
Holliday Junction Arrays Visualized by Atomic Force Microscopy". Journal of the American Chemical Society
121 (23): 5437-5443. doi: 10.1021/ja9900398 (http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863
(http://worldcat.org/issn/0002-7863).

• Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping; Ding, Baoguan;
Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie & Seeman, Nadrian C. (2006). "Double
cohesion in structural DNA nanotechnology". Organic and Biomolecular Chemistry 4: 3414-3419. doi:
10. 1039/b605212f (http://dx.doi.org/10.1039/b605212f).

• Mathieu, Frederick; Liao, Sniping; Kopatsch, Jens; Wang, Tong; Mao, Chengde & Seeman, Nadrian C. (April
2005). "Six-Helix Bundles Designed from DNA". Nano Letters 5 (4): 661-665. doi: 10.1021/nl050084f (http://
dx.doi.org/10.1021/nl050084f). ISSN 1530-6984 (http://worldcat.org/issn/1530-6984).

• Rothemund, Paul W. K. (2006). "Folding DNA to create nanoscale shapes and patterns". Nature 440:
297-302. doi: 10.1038/nature04586 (http://dx.doi.org/10.1038/nature04586). ISSN 0028-0836 (http://
worldcat.org/issn/0028-0836).

• Zhang, Yuwen; Seeman, Nadrian C. (1994). "Construction of a DNA-truncated octahedron". Journal of the
American Chemical Society 116 (5): 1661-1669. doi: 10.1021/ja00084a006 (http://dx.doi.org/10.1021/
ja00084a006). ISSN 0002-7863 (http://worldcat.org/issn/0002-7863).

• Shih, William M. ; Quispe, Joel D. ; Joyce, Gerald F. (12 February 2004). "A 1.7-kilobase single-stranded DNA
that folds into a nanoscale octahedron". Nature 427: 618-621. doi: 10.1038/nature02307 (http://dx.doi.
org/10. 1038/nature02307). ISSN 0028-0836 (http://worldcat.org/issn/0028-0836).

• Goodman, R.P.; Schaap, I.A.T.; Tardin, C.F.; Erben, CM.; Berry, R.M.; Schmidt, C.F.; Turberfield, A.J. (9
December 2005). "Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication".
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• Yurke, Bernard; Turberfield, Andrew J.; Mills, Allen P., Jr; Simmel, Friedrich C. & Neumann, Jennifer L. (10
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DNA nanotechnology 210

0028-0836).

• Mao, Chengde; Sun, Weiqiong; Shen, Zhiyong & Seeman, Nadrian C. (14 January 1999). "A DNA
Nanomechanical Device Based on the B-Z Transition". Nature 397: 144-146. doi: 10.1038/16437 (http://dx.
doi.org/10. 1038/16437). ISSN .

• Yan, Hao; Zhang, Xiaoping; Shen, Zhiyong & Seeman, Nadrian C. (3 January 2002). "A robust DNA
mechanical device controlled by hybridization topology". Nature 415: 62-65. doi: 10.1038/41 5062a (http://
dx.doi.org/10.1038/415062a). ISSN .

[11] DNA Logic Gates (https://digamma.cs.unm.edu/wiki/bin/view/McogPublicWeb/MolecularLogicGates)
[12] (http://www.duke.edu/~jmel7/Joshua_E._Mendoza-Elias/Research_Ideas.html)
[13] MAYA II (https://digamma.cs.unm.edu/wiki/bin/view/McogPublicWeb/MolecularAutomataMAYAII)
[14] http://dx.doi.org/10.1371/journal.pbio.0020424

• Rothemund, Paul W. K.; Papadakis, Nick & Winfree, Erik (December 2004). "Algorithmic Self-Assembly of
DNA Sierpinski Triangles". PLoS Biology 2 (12): 2041-2053. doi: 10. 1371/journal.pbio. 0020424 (http://dx.
doi.org/10.1371/journal.pbio.0020424). ISSN 1544-9173 (http://worldcat.org/issn/1544-9173).

• Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A Self-Assembling
Molecular-Scale Memory Device". Protein Engineering 1 (4): 295-300. ISSN 0269-2139 (http://worldcat.
org/issn/0269-2139). Link (http://peds.oxfordjournals.Org/cgi/content/abstract/l/4/295)

• Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl, Richard A. & Seeman
Nadrian C. (2006). "2D Nanoparticle Arrays Show the Organizational Power of Robust DNA Motifs". Nano
Letters 6: 1502-1504. doi: 10.1021/nl060994c (http://dx.doi.org/10.1021/nl060994c). ISSN 1530-6984
(http://worldcat.org/issn/1530-6984).

• Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single Molecules on DNA
Nanostructures". Angewandte Chemie 46 (42): 7956-7959. doi: 10.1002/anie.200702767 (http://dx.doi.
org/10. 1002/anie. 200702767). ISSN 0570-0833 (http://worldcat.org/issn/0570-0833).

[17] Park, Sung Ha; Sung Ha Park, Constantin Pistol, Sang Jung Ahn, John H. Reif, Alvin R. Lebeck, Chris Dwyer,
Thomas H. LaBean (October 2006).

"http://www3.interscience.wiley.com/journal/113390879/abstractlFinite-Size, Fully Addressable DNA Tile
Lattices Formed by Hierarchical Assembly Procedures". Angewandte Chemie 118 (40): 749-753. doi:
10. 1002/ange. 200690141 (http://dx.doi.org/10.1002/ange.200690141). ISSN 1521-3757 (http://worldcat.
org/issn/1 52 1-3757). http://www3.interscience.wiley.com/journal/113390879/abstract.

[18] Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003).
"http://www.sciencemag.org/cgi/content/abstract/sci;302/5649/1380|DNA-Templated Carbon Nanotube
Field-Effect Transistor". Science 302 (6549): 1380-1382. doi: 10. 1126/science. 1091022 (http://dx.doi.org/10.
1126/science. 1091022). ISSN 1095-9203 (http://worldcat.org/issn/1095-9203). http://www.sciencemag.
org/cgi/content/abstract/sci;302/5649/1380.

[19] http ://www. chem.purdue. edu/people/faculty/faculty. asp?itemID =46

[20] http://www.cs.duke.edu/~reif/BMC/Reif.BMCproject.html

[21] http ://seemanlab4 . chem. nyu. edu/

[22] http://research2.dfci.harvard.edu/shih/SHIH_LAB/Home.html

[23] http://www.physics.ox.ac.uk/cm/people/turberfield.htm

[24] http://dna.caltech.edu/

[25] http ://chemistry. asu . edu/f aculty/haoyan .asp

[26] http://www.bell-labs.com/org/physicalsciences/profiles/yurke.html

[27] http ://coen. boisestate. edu/departments/faculty. asp?ID= 1 34

[28] http://www.cs.duke.edu/~thl/

[29] http://www.agilemolecule.com/Ascalaph/Ascalaph_Designer.html

[30] http://cadnano.org

[31] http://www.subirac.com

[32] http://www.nanoengineer-l.net

[33] http://www.isnsce.org/

Molecular self-assembly

211

Molecular self-assembly

Molecular self-assembly is

the process by which

molecules adopt a defined

arrangement without guidance

or management from an

outside source. There are two

types of self-assembly,

intramolecular self-assembly

and intermolecular

self-assembly. Most often the

term molecular self-assembly refers to intermolecular

intramolecular analog is more commonly called folding.

An example of a molecular self-assembly through hydrogen bonds

reported by Meijer and coworkers

[11

self-assembly, while the

Supramolecular Systems

Molecular self-assembly is a key concept in supramolecular chemistry ] [ ] [ ] since
assembly of the molecules is directed through noncovalent interactions (e.g., hydrogen
bonding, metal coordination, hydrophobic forces, van der Waals forces, n-n interactions,
and/or electrostatic) as well as electromagnetic interactions. Common examples include the
formation of micelles, vesicles, liquid crystal phases, and Langmuir monolayers by
surfactant molecules. Further examples of supramolecular assemblies demonstrate that a
variety of different shapes and sizes can be obtained using molecular self-assembly.

Molecular self-assembly has allowed the construction of challenging molecular topologies.
An example are Borromean rings, interlocking rings wherein removal of one ring unlocks
each of the other rings. DNA has been used to prepare a molecular analog of Borromean
rings. More recently, a similar structure has been prepared using non-biological building
blocks. [7]

Biological Systems

Molecular self-assembly is crucial to the function of cells. It is exhibited in the self-assembly
of lipids to form the membrane, the formation of double helical DNA through hydrogen
bonding of the individual strands, and the assembly of proteins to form quaternary
structures. Molecular self-assembly of incorrectly folded proteins into insoluble amyloid
fibers is responsible for infectious prion-related neurodegenerative diseases.

Molecular self-assembly

212

Nanotechnology

Molecular self-assembly is an

important aspect of bottom-up

approaches to

nanotechnology. Using

molecular self-assembly the

final (desired) structure is

programmed in the shape and

functional groups of the

molecules. Self-assembly is

referred to as a 'bottom-up'

manufacturing technique in

contrast to a 'top-down'

technique such as lithography

where the desired final

structure is carved from a

larger block of matter. In the speculative vision of molecular nanotechnology, microchips of

the future might be made by molecular self-assembly. An advantage to constructing

nanostructure using molecular self-assembly for biological materials is that they will

degrade back into individual molecules that can be broken down by the body.

100 nm

The DNA structure at left (schematic shown) will self-assemble into
the structure visualized by atomic force microscopy at right. Image
from Strong.

DNA nanotechnology

DNA nanotechnology is an area of current research that uses the bottom-up, self-assembly
approach for nanotechnological goals. DNA nanotechnology uses the unique molecular
recognition properties of DNA and other nucleic acids to create self-assembling branched
DNA complexes with useful properties. DNA is thus used as a structural material rather
than as a carrier of biological information, to make structures such as two-dimensional
periodic lattices (both tile-based as well as using the "DNA origami" method) and
three-dimensional structures in the shapes of polyhedra. These DNA structures have

also been used to template the assembly of other molecules such as gold nanoparticles

n 21
and streptavidin proteins.

,[ll]

See also

• Supramolecular assembly

• Supramolecular chemistry

References

[1] F. H. Beijer, H. Kooijman, A. L. Spek, R. P. Sijbesma & E. W. Meijer (1998). "Self-Complementarity Achieved

through Quadruple Hydrogen Bonding". Angew. Chem. Int. Ed. 37 (1-2): 75-78. doi:

10. 1002/(SICI)1521-3773(19980202)37:1/2<75:AID-ANIE75>3.0.CO;2-R (http://dx.doi.org/10.1002/

(SICI)1521-3773(19980202)37:1/2<75::AID-ANIE75>3.0.CO;2-R).
[2] J.-M. Lehn (1988). "Perspectives in Supramolecular Chemistry-From Molecular Recognition towards Molecular

Information Processing and Self-Organization". Angew. Chem. Int. Ed. Engl. 27 (11): 89-121. doi:

10. 1002/anie. 198800891 (http://dx.doi.org/10.1002/anie.198800891).
[3] J.-M. Lehn (1990). "Supramolecular Chemistry-Scope and Perspectives: Molecules, Supermolecules, and

Molecular Devices (Nobel Lecture)". Angew. Chem. Int. Ed. Engl. 29 (11): 1304-1319. doi:

10. 1002/anie. 199013041 (http://dx.doi.org/10.1002/anie.199013041).

Molecular self-assembly 213

[4] Lehn, J.-M.. Supramolecular Chemistry: Concepts and Perspectives. Wiley-VCH. ISBN 978-3-527-29311-7.
[5] Rosen, Milton J. (2004). Surfactants and interfacial phenomena. Hoboken, NJ: Wiley-Interscience. ISBN

978-0-471-47818-8.
[6] C. Mao, W. Sun & N. C. Seeman (1997), "Assembly of Borromean rings from DNA", Nature 386 (6621):

137-138, doi: 10.1038/386137b0 (http://dx.doi.org/10.1038/386137b0)
[7] K. S. Chichak, S. J. Cantrill, A. R. Pease, S.-H. Chen, G. W. V. Cave, J. L. Atwood & J. F. Stoddart (2004),

"Molecular Borromean Rings", Science 304 (5675): 1308-1312, doi: 10.1 126/science. 1096914 (http://dx.doi.

org/10. 1126/science. 1096914), PMID 15166376
[8] M. Strong (2004). "Protein Nanomachines". PLoS Biol. 2 (3): e73-e74. doi: 10. 1371/journal.pbio. 0020073

(http://dx.doi.org/10.1371/journal.pbio.0020073).
[9] N. C. Seeman (2003). "DNA in a material world". Nature 421 (6921): 427-431. doi: 10.1038/nature01406

(http://dx.doi.org/10.1038/nature01406).
[10] J. Chen & N. C. Seeman (1991), "http://www.palgrave-journals.com/doifinder/10.1038/350631a0ISynthesis

from DNA of a molecule with the connectivity of a cube" (w), Nature 350 (6319): 631-633, doi:

10.1038/350631a0 (http://dx.doi.org/10.1038/350631a0), http://www.palgrave-journals.com/doifinder/

10.1038/350631a0
[11] C. A. Mirkin, R. L. Letsinger, R. C. Mucic & J. J. Storhoff (1996). "A DNA-based method for rationally

assembling nanoparticles into macroscopic materials". Nature 382 (6592): 607-609. doi: 10.1038/382607a0

(http://dx.doi.org/10.1038/382607a0).
[12] H. Yan, S. H. Park, G. Finkelstein, J. H. Reif & T. H. Labean (2003),

"http://www.sciencemag.org/cgi/content/abstract/301/5641/1882IDNA-Templated Self-Assembly of Protein

Arrays and Highly Conductive Nanowires", Science 301 (5641): 1882-1884, doi: 10.1126/science.l089389

(http://dx.doi.org/10.1126/science.1089389), PMID 14512621, http://www.sciencemag.org/cgi/content/

abstract/301/5641/1882

External and further reading

• H.E. Hoster, M. Roos, A. Breitruck, C. Meier, K. Tonigold, T. Waldmann, U. Ziener, K.
Landfester, R.J. Behm, Structure Formation in Bis(terpyridine)Derivative Adlayers -
Molecule-Substrate vs. Molecule-Molecule Interactions, Langmuir 23 (2007) 11570

• Molecular Self-Assembly papers (http://www.esi-topics.com/msa/)

• Beyond molecules: Self-assembly of mesoscopic and macroscopic components (http://
www.pubmedcentral.nih.gov/articlerender.fcgi?artid=122665)

• Whitesides, G. M. & Grzyboski, B. (2002) Science 295, 2418-2421.

• Rothemund PWK, Papadakis N, Winfree E (2004) Algorithmic Self-Assembly of DNA
Sierpinski Triangles (http://biology.plosjournals.org/perlserv/
?request=get-document&doi=10. 1371/journal.pbio. 0020424). PLoS Biol 2(12)

• C2 Wiki: Self Assembly from a computer programming perspective (http://c2.com/cgi/
wiki? Self Assembly) .

• Mohammadzadegan R, Sheikhi MH (2007) DNA Nano-Gears (http://www.informaworld.
com/openurl?genre=article&issn= 0892-7022 &volume=33&issue=13&spage= 1071)
Molecular Simulation 33(13); 1071-1081.

• Structure and Dynamics of Organic Nanostructures (http://www.uni-ulm.de/~hhoster/
personal/selfassembly.htm)

• Metal organic coordination networks of oligopyridines and Cu on graphite (http://www.
uni-ulm.de/~hhoster/personal/metal_organic.htm)

• "Challenges and breakthroughs in recent research on self-assembly" Sci. Technol. Adv.
Mater. 9 No 1(2008) 014109 (96 pages) free download (http://dx.doi.org/10.1088/
1468-6996/9/1/014109)

Cell signaling

214

Cell signaling

Cell signaling is part of a complex system of

communication that governs basic cellular activities

rii
and coordinates cell actions. The ability of cells to

perceive and correctly respond to their

microenvironment is the basis of development, tissue

repair, and immunity as well as normal tissue

homeostasis. Errors in cellular information processing

are responsible for diseases such as cancer,

autoimmunity, and diabetes. By understanding cell

signaling, diseases may be treated effectively and,

theoretically, artificial tissues may be yielded.

Traditional work in biology has focused on studying

individual parts of cell signaling pathways. Systems

biology research helps us to understand the underlying

structure of cell signaling networks and how changes in

these networks may affect the transmission and flow of

information. Such networks are complex systems in

their organization and may exhibit a number of

emergent properties including bistability and

ultrasensitivity. Analysis of cell signaling networks requires a combination of experimental

and theoretical approaches including the development and analysis of simulations and

modelling.

Unicellular and multicellular organism cell signaling

Cell signaling has been most extensively studied in the

context of human diseases and signaling between cells

of a single organism. However, cell signaling may also

occur between the cells of two different organisms. In

many mammals, early embryo cells exchange signals

with cells of the uterus. In the human gastrointestinal

tract, bacteria exchange signals with each other and

with human epithelial and immune system cells. For

the yeast Saccharomyces cerevisiae during mating,

some cells send a peptide signal (mating factor Figure l . Example of signaling

pheromones) into their environment. The mating factor between bacteria. Salmonella

peptide may bind to a cell surface receptor on other ententidis uses acyl-homosenne

„ , . , ., ,. r 51 lactone for Quorum sensing (see:

yeast cells and induce them to prepare for mating. 1 , ,_ _, . , _ [2],

Inter-Bacterial Communication )

Cell signaling

215

Types of signals

'Suppressor e( Sp i)
of Hairless

Figure 2. Notch-mediated juxtacrine
signal between adjacent cells.

Cells communicate with each other via direct contact
(juxtacrine signaling), over short distances (paracrine
signaling), or over large distances and/or scales
(endocrine signaling).

Some cell-to-cell communication requires direct cell-cell
contact. Some cells can form gap junctions that connect
their cytoplasm to the cytoplasm of adjacent cells. In
cardiac muscle, gap junctions between adjacent cells
allows for action potential propagation from the cardiac
pacemaker region of the heart to spread and
coordinately cause contraction of the heart.

The Notch signaling mechanism is an example of
juxtacrine signalling (also known as contact dependent
signaling) in which two adjacent cells must make physical contact in order to communicate.
This requirement for direct contact allows for very precise control of cell differentiation
during embryonic development. In the worm Caenorhabditis elegans, two cells of the
developing gonad each have an equal chance of terminally differentiating or becoming a
uterine precursor cell that continues to divide. The choice of which cell continues to divide
is controlled by competition of cell surface signals. One cell will happen to produce more of
a cell surface protein that activates the Notch receptor on the adjacent cell. This activates a
feedback loop or system that reduces Notch expression in the cell that will differentiate and
increases Notch on the surface of the cell that continues as a stem cell.

[6]

Many cell signals are carried by molecules that are released by one cell and move to make
contact with another cell. Endocrine signals are called hormones. Hormones are produced
by endocrine cells and they travel through the blood to reach all parts of the body.
Specificity of signaling can be controlled if only some cells can respond to a particular
hormone. Paracrine signals target only cells in the vicinity of the emitting cell.
Neurotransmitters represent an example. Some signaling molecules can function as both a
hormone and a neurotransmitter. For example, epinephrine and norepinephrine can
function as hormones when released from the adrenal gland and are transported to the
heart by way of the blood stream. Norepinephrine can also be produced by neurons to

T71

function as a neurotransmitter within the brain. Estrogen can be released by the ovary
and function as a hormone or act locally via paracrine or autocrine signaling.

Receptors for cell signals

Cells receive information from their environment through a class of proteins known as
receptors. Notch is a cell surface protein that functions as a receptor. Animals have a small
set of genes that code for signaling proteins that interact specifically with Notch receptors
and stimulate a response in cells that express Notch on their surface. Molecules that
activate (or, in some cases, inhibit) receptors can be classified as hormones,
neurotransmitters, cytokines, growth factors but all of these are called receptor ligands.
The details of ligand-receptor interactions are fundamental to cell signaling.

As shown in Figure 2 (above, left), Notch acts as a receptor for ligands that are expressed
on adjacent cells. While many receptors are cell surface proteins, some are found inside

Cell signaling

216

cells. For example, estrogen is a hydrophobic molecule that can pass through the lipid
bilayer of cell surface membranes. Estrogen receptors inside cells of the uterus can be
activated by estrogen that comes from the ovaries, enters the target cells, and binds to
estrogen receptors.

Other signaling molecules are unable to permeate the hydrophobic cell membrane due to
their hydrophilic nature, so their target receptor is expressed on the membrane. When such
signaling molecule activates its receptor, the signal is carried into the cell usually by means
of a second messenger such as cAMP.

Cnsmokine*.

Hormones,

Survival Factors

Tonsfiiitte-is

Growth Factors

leg.lGFt)

[e.g. interteukms.
serotonin, mc.)

[eg.TGFi.:, EGF)

Signaling pathways

In some cases, receptor
activation caused by ligand
binding to a receptor is
directly coupled to the cell's
response to the ligand. For
example, the neurotransmitter
GABA can activate a cell

Cylakines

{e.g.. EPC|

surface receptor that is part of

an ion channel. GABA binding

to a GABA A receptor on a

neuron opens a

chloride-selective ion channel

that is part of the receptor.

GABA A receptor activation

allows negatively-charged

chloride ions to move into the

neuron, which inhibits the

ability of the neuron to produce action potentials. However, for many cell surface receptors,

ligand-receptor interactions are not directly linked to the cell's response. The activated

receptor must first interact with other proteins inside the cell before the ultimate

physiological effect of the ligand on the cell's behavior is produced. Often, the behavior of a

chain of several interacting cell proteins is altered following receptor activation. The entire

set of cell changes induced by

Overview of signal transduction pathways.

Cell signaling

217

receptor activation is called a signal transduction mechanism or
pathway.

In the case of Notch-mediated signaling, the signal transduction
mechanism can be relatively simple. As shown in Figure 2 (above,
left), activation of Notch can cause the Notch protein to be altered
by a protease. Part of the Notch protein is released from the cell
surface membrane and can act to change the pattern of gene
transcription in the cell nucleus. This causes the responding cell to
make different proteins, resulting in an altered pattern of cell
behavior. Cell signaling research involves studying the spatial and
temporal dynamics of both receptors and the components of
signaling pathways that are activated by receptors in various cell
types.

transcription nucleus

Figure 3. Diagram

showing key components

of a signal transduction

pathway. See the

MAPK/ERK pathway

article for details.

A more complex signal transduction pathway is shown in Figure 3. This pathway involves
changes of protein-protein interactions inside the cell, induced by an external signal. Many
growth factors bind to receptors at the cell surface and stimulate cells to progress through
the cell cycle and divide. Several of these receptors are kinases that start to phosphorylate
themselves and other proteins when binding to a ligand. This phosphorylation can generate
a binding site for a different protein and thus induce protein-protein interaction. In Figure
3, the ligand (called epidermal growth factor (EGF)) binds to the receptor (called EGFR).
This activates the receptor to phosphorylate itself. The phosphorylated receptor binds to an
adaptor protein (GRB2), which couples the signal to further downstream signaling
processes. For example, one of the signal transduction pathways that are activated is called
the mitogen-activated protein kinase (MAPK) pathway. The signal transduction component
labeled as "MAPK" in the pathway was originally called "ERK," so the pathway is called the
MAPK/ERK pathway. The MAPK protein is an enzyme, a protein kinase that can attach
phosphate to target proteins such as the transcription factor MYC and, thus, alter gene
transcription and, ultimately, cell cycle progression. Many cellular proteins are activated
downstream of the growth factor receptors (such as EGFR) that initiate this signal
transduction pathway.

Cell signaling 218

Some signaling transduction pathways respond differently depending on the amount of
signaling received by the cell. For instance, the hedgehog protein activates different genes,
depending on the amount of hedgehog protein present.

Complex multi-component signal transduction pathways provide opportunities for feedback,
signal amplification, and interactions inside one cell between multiple signals and signaling
pathways.

Classification of intercellular communication

Within endocrinology (the study of intercellular signalling in animals) and the endocrine
system, intercellular signalling is subdivided into the following classifications:

• Endocrine signals are produced by endocrine cells and travel through the blood to reach
all parts of the body.

• Paracrine signals target only cells in the vicinity of the emitting cell. Neurotransmitters
represent an example.

• Autocrine signals affect only cells that are of the same cell type as the emitting cell. An
example for autocrine signals is found in immune cells.

• Juxtacrine signals are transmitted along cell membranes via protein or lipid components
integral to the membrane and are capable of affecting either the emitting cell or cells
immediately adjacent.

See also

• Molecular Cellular Cognition

• Crosstalk (biology)

• MAPK signaling pathway

• Hedgehog signaling pathway

• TGF beta signaling pathway

• JAK-STAT signaling pathway

• cAMP dependent pathway

• Signal transduction

• Systems biology

• Semiotics

• Lipid signaling

References

[1] Witzany, G.lll (2000). Life: The Communicative Structure. Norderstedt, Libri BoD.

[2] http ://www. ars.usda. gov/is/AR/archive/janOO/bactO 1 00. htm

[3] O. A. Mohamed, M. Jonnaert, C. Labelle-Dumais, K. Kuroda, H.J. Clarke and D. Dufort (2005) "Uterine

Wnt/beta-catenin signaling is reguired for implantation" in Proceedings of the National Academy of Sciences of
the United States of America Volume 102, pages 8579-8584. Entrez Pubmed 15930138 (http://www.ncbi.nlm.
nih.gov/entrez/guery.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids= 159301 38).

[4] M.B. Clarke and V. Sperandio (2005) "Events at the host-microbial interface of the gastrointestinal tract III.
Cell-to-cell signaling among microbial flora, poop, and pathogens: there is a whole lot of talking going on" in
American journal of physiology. Gastrointestinal and liver physiology. Volume 288, pages G1105-9. Entrez
Pubmed 15890712 (http ://www. ncbi. nlm. nih. gov/entrez/guery. fcgi?cmd= Retrieve&db =pubmed&
dopt=Abstract&list_uids= 15890712).

[5] J. C. Lin, K. Duell and J. B. Konopka (2004) "A microdomain formed by the extracellular ends of the

transmembrane domains promotes activation of the G protein-coupled alpha-factor receptor" in Molecular Cell
Biology Volume 24, pages 2041-2051. Entrez Pubmed 14966283 (http://www.ncbi.nlm.nih.gov/entrez/

Cell signaling 219

query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids= 14966283).
[6] I. Greenwald (1998) "LIN-12/Notch signaling: lessons from worms and flies" in Genes in Development Volume

12, pages 1751-1762. Entrez Pubmed 9637676 (http://www.ncbi.nlm.nih.gov/entrez/query.

fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=9637676).
[7] M. C. Cartford, A. Samec, M. Fister and P. C. Bickford (2004) "Cerebellar norepinephrine modulates learning

of delay classical eyeblink conditioning: evidence for post-synaptic signaling via PKA" in Learning & memory

Volume 11, pages 732-737. Entrez Pubmed 15537737 (http://www.ncbi.nlm.nih.gov/entrez/query.

fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids= 15537737).
[8] S. Jesmin, C. N. Mowa, I. Sakuma, N. Matsuda, H. Togashi, M. Yoshioka, Y. Hattori and A. Kitabatake (2004)

"Aromatase is abundantly expressed by neonatal rat penis but downregulated in adulthood" in Journal of

Molecular Endocrinology Volume 33, pages 343-359. Entrez Pubmed 15525594 (http://www.ncbi.nlm.nih.

gov/ entrez/ query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids= 1552 5594).

External links

• Signaling Gateway (http://www.signaling-gateway.org) Free summaries of recent
research and the Molecule Pages database (http://www.signaling-gateway.org/
molecule/).

• NCI-Nature Pathway Interaction Database (http://pid.nci.nih.gov): authoritative
information about signaling pathways in human cells.

• Cell Communication (http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Search&
db=books&doptcmdl=GenBookHL&term="Cell+ signaling" +AND+ mboc4[book] +
AND+373842[uid]&rid=mboc4. section. 2743*2793), Chapter 15 in Molecular Biology
of the Cell (http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Search&
db=books&doptcmdl=GenBookHL&term=cell+biology+AND+mboc4[book]+AND +
373693[uid]&rid=mboc4) fourth edition, edited by Bruce Alberts (2002) published by
Garland Science.

• Cell Signaling (http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Search&
db=books&doptcmdl=GenBookHL&term="Cell+ signaling" +AND+ cooper[book] +
AND + 166039[uid]&rid=cooper.chapter.2198), Chapter 13 in The Cell - A Molecular
Approach (http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Search&
db=books&doptcmdl=GenBookHL&term=cell+biology+AND + cooper[book]+AND+
165077[uid]&rid=cooper.chapter.89) second edition, by Geoffrey M. Cooper (2000)
published by Sinauer Associates.

• Cell-to-Cell Signaling (http://www.ncbi.nlm.nih.gov/entrez/query.
fcgi?cmd=Search&db=books&doptcmdl=GenBookHL&term="Cell+ signaling" +AND+
mcb[book]+AND+107116[uid]&rid=mcb.chapter.5687), Chapter 20 in Molecular Cell
Biology (http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Search&db=books&
doptcmdl=GenBookHL&term=cell+biology+AND+mcb[book]+AND+105032[uid]&
rid=mcb. chapter. 145) fourth edition, edited by Harvey Lodish (2000) published by W.
H. Freeman and Company.

• MeSH Intercellular+Signaling+Peptides+and+Proteins (http://www.nlm.nih.gov/cgi/
mesh/2 009/MB_cgi?mode=&term=Intercellular+Signaling+Peptides+and-l- Proteins)

• MeSH Cell+ Communication (http://www.nlm.nih.gov/cgi/mesh/2009/
MB_cgi?mode=&term=Cell+ Communication)

• ESIGNET Research Project (http://www.esignet.net)

• International q-bio Conference on Cellular Information Processing

Molecular evolution 220

Molecular evolution

Molecular evolution is the process of evolution at the scale of DNA, RNA, and proteins.
Molecular evolution emerged as a scientific field in the 1960s as researchers from
molecular biology, evolutionary biology and population genetics sought to understand
recent discoveries on the structure and function of nucleic acids and protein. Some of the
key topics that spurred development of the field have been the evolution of enzyme
function, the use of nucleic acid divergence as a "molecular clock" to study species
divergence, and the origin of non-functional or junk DNA. Recent advances in genomics,
including whole-genome sequencing, high-throughput protein characterization, and
bioinformatics have led to a dramatic increase in studies on the topic. In the 2000s, some of
the active topics have been the role of gene duplication in the emergence of novel gene
function, the extent of adaptive molecular evolution versus neutral drift, and the
identification of molecular changes responsible for various human characteristics especially
those pertaining to infection, disease, and cognition.

Principles of molecular evolution

Mutations

Mutations are permanent, transmissible changes to the genetic material (usually DNA or
RNA) of a cell. Mutations can be caused by copying errors in the genetic material during
cell division and by exposure to radiation, chemicals, or viruses, or can occur deliberately
under cellular control during the processes such as meiosis or hypermutation. Mutations
are considered the driving force of evolution, where less favorable (or deleterious)
mutations are removed from the gene pool by natural selection, while more favorable (or
beneficial) ones tend to accumulate. Neutral mutations do not affect the organism's
chances of survival in its natural environment and can accumulate over time, which might
result in what is known as punctuated equilibrium; the modern interpretation of classic
evolutionary theory.

Causes of change in allele frequency

There are three known processes that affect the survival of a characteristic; or, more
specifically, the frequency of an allele (variant of a gene):

• Genetic drift describes changes in gene frequency that cannot be ascribed to selective
pressures, but are due instead to events that are unrelated to inherited traits. This is
especially important in small mating populations, which simply cannot have enough
offspring to maintain the same gene distribution as the parental generation.

• Gene flow or Migration: or gene admixture is the only one of the agents that makes
populations closer genetically while building larger gene pools.

• Selection, in particular natural selection produced by differential mortality and fertility.
Differential mortality is the survival rate of individuals before their reproductive age. If
they survive, they are then selected further by differential fertility - that is, their total
genetic contribution to the next generation. In this way, the alleles that these surviving
individuals contribute to the gene pool will increase the frequency of those alleles. Sexual
selection, the attraction between mates that results from two genes, one for a feature
and the other determining a preference for that feature, is also very important.

Molecular evolution 221

Molecular study of phylogeny

Molecular systematics is a product of the traditional field of systematics and molecular
genetics. It is the process of using data on the molecular constitution of biological
organisms' DNA, RNA, or both, in order to resolve questions in systematics, i.e. about their
correct scientific classification or taxonomy from the point of view of evolutionary biology.

Molecular systematics has been made possible by the availability of techniques for DNA
sequencing, which allow the determination of the exact sequence of nucleotides or bases in
either DNA or RNA. At present it is still a long and expensive process to sequence the
entire genome of an organism, and this has been done for only a few species. However, it is
quite feasible to determine the sequence of a defined area of a particular chromosome.
Typical molecular systematic analyses require the sequencing of around 1000 base pairs.

The driving forces of evolution

Depending on the relative importance assigned to the various forces of evolution, three

rn
perspectives provide evolutionary explanations for molecular evolution.

While recognizing the importance of random drift for silent mutations, selectionists
hypotheses argue that balancing and positive selection are the driving forces of molecular
evolution. Those hypotheses are often based on the broader view called panselectionism,
the idea that selection is the only force strong enough to explain evolution, relaying random
drift and mutations to minor roles.

Neutralists hypotheses emphasize the importance of mutation, purifying selection and
random genetic drift. The introduction of the neutral theory by Kimura, quickly
followed by King and Jukes' own findings, lead to a fierce debate about the relevance of
neodarwinism at the molecular level. The Neutral theory of molecular evolution states that
most mutations are deleterious and quickly removed by natural selection, but of the
remaining ones, the vast majority are neutral with respect to fitness while the amount of
advantageous mutations is vanishingly small. The fate of neutral mutations are governed by
genetic drift, and contribute to both nucleotide polymorphism and fixed differences
between species.

Mutationists hypotheses emphasize random drift and biases in mutation patterns.
Sueoka was the first to propose a modern mutationist view. He proposed that the variation
in GC content was not the result of positive selection, but a consequence of the GC
mutational pressure.

Related fields

An important area within the study of molecular evolution is the use of molecular data to
determine the correct biological classification of organisms. This is called molecular
systematics or molecular phylogenetics.

Tools and concepts developed in the study of molecular evolution are now commonly used
for comparative genomics and molecular genetics, while the influx of new data from these
fields has been spurring advancement in molecular evolution.

Molecular evolution

222

Key researchers in molecular evolution

Some researchers who have made key contributions to the development of the field:

Motoo Kimura — Neutral theory

Masatoshi Nei — Adaptive evolution

Walter M. Fitch — Phylogenetic reconstruction

Walter Gilbert — RNA world

Joe Felsenstein — Phylogenetic methods

Susumu Ohno — Gene duplication

John H. Gillespie — Mathematics of adaptation

Journals and societies

Journals dedicated to molecular evolution include Molecular Biology and Evolution, Journal
of Molecular Evolution, and Molecular Phylo genetics and Evolution. Research in molecular
evolution is also published in journals of genetics, molecular biology, genomics,
systematics, or evolutionary biology. The Society for Molecular Biology and Evolution L J
publishes the journal "Molecular Biology and Evolution" and holds an annual international
meeting.

See also

History of molecular evolution

Chemical evolution

Evolution

Genetic drift

E. coli long-term evolution experiment

Evolutionary physiology

Neutral theory of molecular evolution

Nucleotide diversity

Parsimony

Population genetics

Selection

• Genomic organization

• Horizontal gene transfer

• Human evolution

• Molecular clock

• Comparative phylogenetics

Molecular evolution 223

Further reading

• Li, W.-H. (2006). Molecular Evolution. Sinauer. ISBN 0878934804.

• Lynch, M. (2007). The Origins of Genome Architecture. Sinauer. ISBN 0878934847.

References

[I] Graur, D. and Li, W.-H. (2000). Fundamentals of molecular evolution. Sinauer.

[2] Gillespie, J. H (1991). The Causes of Molecular Evolution. Oxford University Press, New York. ISBN

0-19-506883-1.
[3] Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge. ISBN

0-521-23109-4.
[4] Kimura, Motoo (1968).

"http://www2.hawaii.edu/~khayes/Journal_Club/fall2006/Kimura_1968_Nature.pdflEvolutionary rate at the

molecular level". Nature 217: 624-626. doi: 10.1038/217624a0 (http://dx.doi.org/10.1038/217624a0). http:/

/www2. hawaii.edu/~khayes/Journal_Club/fall2006/Kimura_l 968_Nature.pdf.
[5] King, J. L. and Jukes, T.H. (1969).

"http://www.blackwellpublishing.com/ridley/classictexts/king.pdflNon-Darwinian Evolution". Science 164:

788-798. doi: 10. 1126/science. 164.3881. 788 (http://dx.doi.org/10.1126/science.164.3881.788). PMID

5767777. http ://www. blackwellpublishing . com/ridley/classictexts/king . p df .
[6] Nachman M. (2006). "Detecting selection at the molecular level" in: Evolutionary Genetics: concepts and case

studies, pp. 103-118.
[7] The nearly neutral theory expanded the neutralist perspective, suggesting that several mutations are nearly

neutral, which means both random drift and natural selection is relevant to their dynamics.
[8] Ohta, T (1992). "The nearly neutral theory of molecular evolution". Annual Review of Ecology and Systematics

23: 263-286. doi: 10. 1146/annurev.es. 23. 110192. 001403 (http://dx.doi.org/10.1146/annurev.es.23.

110192.001403).
[9] Nei, M. (2005). "Selectionism and Neutralism in Molecular Evolution". Molecular Biology and Evolution

22(12): 2318-2342. doi: 10.1093/molbev/msi242 (http://dx.doi.org/10.1093/molbev/msi242). PMID

16120807.
[10] Sueoka, N. (1964). "On the evolution of informational macromolecules". in In: Bryson, V. and Vogel, H.J..

Evolving genes and proteins. Academic Press, New-York. pp. 479-496.

[II] http://www.smbe.org

Molecular phylogenetics 224

Molecular phylogenetics

Molecular phylogenetics, also known as molecular systematics, is the use of the

structure of molecules to gain information on an organism's evolutionary relationships. The
result of a molecular phylogenetic analysis is expressed in a phylogenetic tree.

Techniques and applications

Every living organism contains DNA, RNA, and proteins. Closely related organisms
generally have a high degree of agreement in the molecular structure of these substances,
while the molecules of organisms distantly related usually show a pattern of dissimilarity.
Conserved sequences such mitochondrial DNA are expected to accumulate mutations over
time, and assuming a constant rate of mutation provide a molecular clock for dating
divergence. Molecular phylogeny uses such data to build a "relationship tree" that shows
the probable evolution of various organisms. Not until recent decades, however, has it been
possible to isolate and identify these molecular structures.

The most common approach is the comparison of sequences for genes using sequence
alignment techniques to identify similarity. Another application of molecular phylogeny is in
DNA barcoding, where the species of an individual organism is identified using small
sections of mitochondrial DNA. Another application of the techniques that make this
possible can be seen in the very limited field of human genetics, such as the ever more
popular use of genetic testing to determine a child's paternity, as well as the emergence of
a new branch of criminal forensics focused on evidence known as genetic fingerprinting.

The effect on traditional biological classification schemes in the biological sciences has
been dramatic as well. Work that was once immensely labor- and materials-intensive can
now be done quickly and easily, leading to yet another source of information becoming
available for systematic and taxonomic appraisal. This particular kind of data has become
so popular that taxonomical schemes based solely on molecular data may be encountered.

Theoretical background

Early attempts at molecular systematics were also termed as chemotaxonomy and made use
of proteins, enzymes, carbohydrates and other molecules which were separated and
characterized using techniques such as chromatography. These have been largely replaced
in recent times by DNA sequencing which produces the exact sequences of nucleotides or
bases in either DNA or RNA segments extracted using different techniques. These are
generally considered superior for evolutionary studies since the actions of evolution are
ultimately reflected in the genetic sequences. At present it is still a long and expensive
process to sequence the entire DNA of an organism (its genome), and this has been done
for only a few species. However it is quite feasible to determine the sequence of a defined
area of a particular chromosome. Typical molecular systematic analyses require the
sequencing of around 1000 base pairs. At any location within such a sequence, the bases
found in a given position may vary between organisms. The particular sequence found in a
given organism is referred to as its haplotype. In principle, since there are four base types,
with 1000 base pairs, we could have 4 distinct haplotypes. However, for organisms

within a particular species or in a group of related species, it has been found empirically
that only a minority of sites show any variation at all and most of the variations that are

Molecular phylogenetics 225

found are correlated, so that the number of distinct haplotypes that are found is relatively
small.

In a molecular systematic analysis, the haplotypes are determined for a defined area of
genetic material; ideally a substantial sample of individuals of the target species or other
taxon are used however many current studies are based on single individuals. Haplotypes of
individuals of closely related, but supposedly different, taxa are also determined. Finally,
haplotypes from a smaller number of individuals from a definitely different taxon are
determined: these are referred to as an out group. The base sequences for the haplotypes
are then compared. In the simplest case, the difference between two haplotypes is assessed
by counting the number of locations where they have different bases: this is referred to as
the number of substitutions (other kinds of differences between haplotypes can also occur,
for example the insertion of a section of nucleic acid in one haplotype that is not present in
another). Usually the difference between organisms is re-expressed as a percentage
divergence, by dividing the number of substitutions by the number of base pairs analysed:
the hope is that this measure will be independent of the location and length of the section
of DNA that is sequenced.

An older and superseded approach was to determine the divergences between the
genotypes of individuals by DNA-DNA hybridisation. The advantage claimed for using
hybridisation rather than gene sequencing was that it was based on the entire genotype,
rather than on particular sections of DNA. Modern sequence comparison techniques
overcome this objection by the use of multiple sequences.

Once the divergences between all pairs of samples have been determined, the resulting
triangular matrix of differences is submitted to some form of statistical cluster analysis, and
the resulting dendrogram is examined in order to see whether the samples cluster in the
way that would be expected from current ideas about the taxonomy of the group, or not.
Any group of haplotypes that are all more similar to one another than any of them is to any
other haplotype may be said to constitute a clade. Statistical techniques such as
bootstrapping and jackknifing help in providing reliability estimates for the positions of
haplotypes within the evolutionary trees.

Characteristics and assumptions of molecular systematics

This example illustrates several characteristics of molecular systematics and its underlying
assumptions.

1. Molecular systematics is an essentially cladistic approach: it assumes that classification
must correspond to phylogenetic descent, and that all valid taxa must be monophyletic.

2. Molecular systematics often uses the molecular clock assumption that quantitative
similarity of genotype is a sufficient measure of the recency of genetic divergence.
Particularly in relation to speciation, this assumption could be wrong if either

1 . some relatively small genotypic modification acted to prevent interbreeding between
two groups of organisms, or

2. in different subgroups of the organisms being considered, genetic modification
proceeded at different rates.

3. In animals, it is often convenient to use mitochondrial DNA for molecular systematic
analysis. However, because in mammals mitochondria are inherited only from the
mother, this is not fully satisfactory, because inheritance in the paternal line might not be
detected: in the example above, Vila et al. cite more limited studies with chromosomal

Molecular phylogenetics 226

DNA that support their conclusions.

These characteristics and assumptions are not wholly uncontroversial among biological
systematists. As a cladistic method, molecular systematics is open to the same criticisms as
cladistics in general. It can also be argued that it is a mistake to replace a classification
based on visible and ecologically relevant characteristics by one based on genetic details
that may not even be expressed in the phenotype. However the molecular approach to
systematics, and its underlying assumptions, are gaining increasing acceptance. As gene
sequencing becomes easier and cheaper, molecular systematics is being applied to more
and more groups, and in some cases is leading to radical revisions of accepted taxonomies.

History of molecular phylogenetics

The theoretical frameworks for molecular systematics were laid in the 1960s in the works
of Emile Zuckerkandl, Emanuel Margoliash, Linus Pauling and Walter M. Fitch.
Applications of molecular systematics were pioneered by Charles G. Sibley (birds), Herbert
C. Dessauer (herpetology), and Morris Goodman (primates), followed by Allan C. Wilson,
Robert K. Selander, and John C. Avise (who studied various groups). Work with protein
electrophoresis began around 1956. Although the results were not quantitative and did not
initially improve on morphological classification, they provided tantalizing hints that
long-held notions of the classifications of birds, for example, needed substantial revision. In

T21

the period of 1974-1986, DNA-DNA hybridization was the dominant technique.

Further reading

• Felsenstein, J. 2004. Inferring phytogenies. Sinauer Associates Incorporated. ISBN
0-87893-177-5.

• Hillis, D. M. & Moritz, C. 1996. Molecular systematics. 2nd ed. Sinauer Associates
Incorporated. ISBN 0-87893-282-8.

• Page, R. D. M. & Holmes, E. C. 1998. Molecular evolution: a phylogenetic approach.
Blackwell Science, Oxford. ISBN 0-86542-889-1.

References

[1] Edna Suarez-Diaz & Victor H. Anaya-Munoz (2008) History, objectivity, and the construction of molecular

phylogenies. Stud. Hist. Phil. Biol. & Biomed. Sci. 39:451-468
[2] Ahlquist, Jon E., 1999: Charles G. Sibley: A commentary on 30 years of collaboration. The Auk, vol. 116, no. 3

(July 1999). A PDF or DjVu version of this article can be downloaded from the issue's table of contents page

(http ://elibrary. unm. edu/sora/Auk/vl 1 6n03/index. php) .

See also

• molecular evolution

• computational phylogenetics

• PhyloCode

Molecular phylogenetics 227

External links

• NCBI - Systematics and Molecular Phylogenetics (http://www.ncbi.nlm.nih.gov/
About/primer/p hylo.html)

Computational phylogenetics

Computational phylogenetics is the application of computational algorithms, methods
and programs to phylogenetic analyses. The goal is to assemble a phylogenetic tree
representing a hypothesis about the evolutionary ancestry of a set of genes, species, or
other taxa. For example, these techniques have been used to explore the family tree of
hominid species and the relationships between specific genes shared by many types of
organisms. ^ Traditional phylogenetics relies on morphological data obtained by measuring
and quantifying the phenotypic properties of representative organisms, while the more
recent field of molecular phylogenetics uses nucleotide sequences encoding genes or amino
acid sequences encoding proteins as the basis for classification. Many forms of molecular
phylogenetics are closely related to and make extensive use of sequence alignment in
constructing and refining phylogenetic trees, which are used to classify the evolutionary
relationships between homologous genes represented in the genomes of divergent species.
The phylogenetic trees constructed by computational methods are unlikely to perfectly
reproduce the evolutionary tree that represents the historical relationships between the
species being analyzed. The historical species tree may also differ from the historical tree
of an individual homologous gene shared by those species.

Producing a phylogenetic tree requires a measure of homology among the characteristics
shared by the taxa being compared. In morphological studies, this requires explicit
decisions about which physical characteristics to measure and how to use them to encode
distinct states corresponding to the input taxa. In molecular studies, a primary problem is
in producing a multiple sequence alignment (MSA) between the genes or amino acid
sequences of interest. Progressive sequence alignment methods produce a phylogenetic
tree by necessity because they incorporate new sequences into the calculated alignment in
order of genetic distance. Although a phylogenetic tree can always be constructed from an
MSA, phylogenetics methods such as maximum parsimony and maximum likelihood do not
require the production of an initial or concurrent MSA.

Types of phylogenetic trees

Phylogenetic trees generated by computational phylogenetics can be either rooted or
unrooted depending on the input data and the algorithm used. A rooted tree is a directed
graph that explicitly identifies a most recent common ancestor (MRCA), usually an imputed
sequence that is not represented in the input. Genetic distance measures can be used to
plot a tree with the input sequences as leaf nodes and their distances from the root
proportional to their genetic distance from the hypothesized MRCA. Identification of a root
usually requires the inclusion in the input data of at least one "outgroup" known to be only
distantly related to the sequences of interest.

By contrast, unrooted trees plot the distances and relationships between input sequences
without making assumptions regarding their descent. An unrooted tree can always be
produced from a rooted tree, but a root cannot usually be placed on an unrooted tree

Computational phylogenetics 228

without additional data on divergence rates, such as the assumption of the molecular clock
hypothesis. - 1

The set of all possible phylogenetic trees for a given group of input sequences can be
conceptualized as a discretely defined multidimensional "tree space" through which search
paths can be traced by optimization algorithms. Although counting the total number of
trees for a nontrivial number of input sequences can be complicated by variations in the
definition of a tree topology, it is always true that there are more rooted than unrooted
trees for a given number of inputs and choice of parameters. ^

Coding characters and defining homology

Morphological analysis

The basic problem in morphological phylogenetics is the assembly of a matrix representing
a mapping from each of the taxa being compared to representative measurements for each
of the phenotypic characteristics being used as a classifier. The types of phenotypic data
used to construct this matrix depend on the taxa being compared; for individual species,
they may involve measurements of average body size, lengths or sizes of particular bones or
other physical features, or even behavioral manifestations. Of course, since not every
possible phenotypic characteristic could be measured and encoded for analysis, the
selection of which features to measure is a major inherent obstacle to the method. The
decision of which traits to use as a basis for the matrix necessarily represents a hypothesis
about which traits of a species or higher taxon are evolutionarily relevant. Morphological
studies can be confounded by examples of convergent evolution of phenotypes. A major
challenge in constructing useful classes is the high likelihood of inter-taxon overlap in the
distribution of the phenotype's variation. The inclusion of extinct taxa in morphological
analysis is often difficult due to absence of or incomplete fossil records, but has been shown
to have a significant effect on the trees produced; in one study only the inclusion of extinct
species of apes produced a morphologically derived tree that was consistent with that
produced from molecular data.

Some phenotypic classifications, particularly those used when analyzing very diverse
groups of taxa, are discrete and unambiguous; classifying organisms as possessing or
lacking a tail, for example, is straightforward in the majority of cases, as is counting
features such as eyes or vertebrae. However, the most appropriate representation of
continuously varying phenotypic measurements is a controversial problem without a
general solution. A common method is simply to sort the measurements of interest into two
or more classes, rendering continuous observed variation as discretely classifiable (e.g., all
examples with humerus bones longer than a given cutoff are scored as members of one
state, and all members whose humerus bones are shorter than the cutoff are scored as
members of a second state). This results in an easily manipulated data set but has been
criticized for poor reporting of the basis for the class definitions and for sacrificing
information compared to methods that use a continuous weighted distribution of
measurements.

Because morphological data is extremely labor-intensive to collect, whether from literature
sources or from field observations, reuse of previously compiled data matrices is not
uncommon, although this may propagate flaws in the original matrix into multiple
derivative analyses.

Computational phylogenetics 229

Molecular analysis

The problem of character coding is very different in molecular analyses, as the characters
in biological sequence data are immediate and discretely defined - distinct nucleotides in
DNA or RNA sequences and distinct amino acids in protein sequences. However, defining
homology can be challenging due to the inherent difficulties of multiple sequence
alignment. For a given gapped MSA, several rooted phylogenetic trees can be constructed
that vary in their interpretations of which changes are "mutations" versus ancestral
characters, and which events are insertion mutations or deletion mutations. For example,
given only a pairwise alignment with a gap region, it is impossible to determine whether
one sequence bears an insertion mutation or the other carries a deletion. The problem is
magnified in MSAs with unaligned and nonoverlapping gaps. In practice, sizable regions of
a calculated alignment may be discounted in phylogenetic tree construction to avoid
integrating noisy data into the tree calculation.

Distance-matrix methods

Distance-matrix methods of phylogenetic analysis explicitly rely on a measure of "genetic
distance" between the sequences being classified, and therefore they require an MSA as an
input. Distance is often defined as the fraction of mismatches at aligned positions, with
gaps either ignored or counted as mismatches. Distance methods attempt to construct an
all-to-all matrix from the sequence query set describing the distance between each
sequence pair. From this is constructed a phylogenetic tree that places closely related
sequences under the same interior node and whose branch lengths closely reproduce the
observed distances between sequences. Distance-matrix methods may produce either
rooted or unrooted trees, depending on the algorithm used to calculate them. They are
frequently used as the basis for progressive and iterative types of multiple sequence
alignments. The main disadvantage of distance-matrix methods is their inability to
efficiently use information about local high-variation regions that appear across multiple
subtrees.

Neighbor-joining

Neighbor-joining methods apply general data clustering techniques to sequence analysis
using genetic distance as a clustering metric. The simple neighbor-joining method produces
unrooted trees, but it does not assume a constant rate of evolution (i.e., a molecular clock)
across lineages. Its relative, UPGMA (Unweighted Pair Group Method with Arithmetic
mean) produces rooted trees and requires a constant-rate assumption - that is, it assumes
an ultrametric tree in which the distances from the root to every branch tip are equal.

Fitch-Margoliash method

The Fitch-Margoliash method uses a weighted least squares method for clustering based on
genetic distance. Closely related sequences are given more weight in the tree
construction process to correct for the increased inaccuracy in measuring distances
between distantly related sequences. The distances used as input to the algorithm must be
normalized to prevent large artifacts in computing relationships between closely related
and distantly related groups. The distances calculated by this method must be linear; the
linearity criterion for distances requires that the expected values of the branch lengths for
two individual branches must equal the expected value of the sum of the two branch

Computational phylogenetics 230

distances - a property that applies to biological sequences only when they have been
corrected for the possibility of back mutations at individual sites. This correction is done
through the use of a substitution matrix such as that derived from the Jukes-Cantor model
of DNA evolution. The distance correction is only necessary in practice when the evolution
rates differ among branches . *

The least-squares criterion applied to these distances is more accurate but less efficient
than the neighbor-joining methods. An additional improvement that corrects for
correlations between distances that arise from many closely related sequences in the data
set can also be applied at increased computational cost. Finding the optimal least-squares
tree with any correction factor is NP-complete, so heuristic search methods like those
used in maximum-parsimony analysis are applied to the search through tree space.

Using outgroups

Independent information about the relationship between sequences or groups can be used
to help reduce the tree search space and root unrooted trees. Standard usage of
distance-matrix methods involves the inclusion of at least one outgroup sequence known to
be only distantly related to the sequences of interest in the query set. This usage can be
seen as a type of experimental control. If the outgroup has been appropriately chosen, it
will have a much greater genetic distance and thus a longer branch length than any other
sequence, and it will appear near the root of a rooted tree. Choosing an appropriate
outgroup requires the selection of a sequence that is moderately related to the sequences
of interest; too close a relationship defeats the purpose of the outgroup and too distant adds
noise to the analysis. Care should also be taken to avoid situations in which the species
from which the sequences were taken are distantly related, but the gene encoded by the
sequences is highly conserved across lineages. Horizontal gene transfer, especially between
otherwise divergent bacteria, can also confound outgroup usage.

Maximum parsimony

Maximum parsimony (MP) is a method of identifying the potential phylogenetic tree that
requires the smallest total number of evolutionary events to explain the observed sequence
data. Some ways of scoring trees also include a "cost" associated with particular types of
evolutionary events and attempt to locate the tree with the smallest total cost. This is a
useful approach in cases where not every possible type of event is equally likely - for
example, when particular nucleotides or amino acids are known to be more mutable than
others.

The most naive way of identifying the most parsimonious tree is simple enumeration -
considering each possible tree in succession and searching for the tree with the smallest
score. However, this is only possible for a relatively small number of sequences or species
because the problem of identifying the most parsimonious tree is known to be NP-hard; [ ]
consequently a number of heuristic search methods for optimization have been developed
to locate a highly parsimonious tree, if not the most optimal in the set. Most such methods
involve a steepest descent-style minimization mechanism operating on a tree
rearrangement criterion.

Computational phylogenetics 231

Branch and bound

The branch and bound algorithm is a general method used to increase the efficiency of
searches for near-optimal solutions of NP-hard problems first applied to phylogenetics in
the early 1980s. Branch and bound is particularly well suited to phylogenetic tree
construction because it inherently requires dividing a problem into a tree structure as it
subdivides the problem space into smaller regions. As its name implies, it requires as input
both a branching rule (in the case of phylogenetics, the addition of the next species or
sequence to the tree) and a bound (a rule that excludes certain regions of the search space
from consideration, thereby assuming that the optimal solution cannot occupy that region).
Identifying a good bound is the most challenging aspect of the algorithm's application to
phylogenetics. A simple way of defining the bound is a maximum number of assumed
evolutionary changes allowed per tree. A set of criteria known as Zharkikh's rules
severely limit the search space by defining characteristics shared by all candidate "most
parsimonious" trees. The two most basic rules require the elimination of all but one
redundant sequence (for cases where multiple observations have produced identical data)
and the elimination of character sites at which two or more states do not occur in at least
two species. Under ideal conditions these rules and their associated algorithm would
completely define a tree.

Sankoff-Morel-Cedergren algorithm

The Sankoff-Morel-Cedergren algorithm was among the first published methods to

ri o]

simultaneously produce an MSA and a phylogenetic tree for nucleotide sequences. 1 J The
method uses a maximum parsimony calculation in conjunction with a scoring function that
penalizes gaps and mismatches, thereby favoring the tree that introduces a minimal
number of such events. The imputed sequences at the interior nodes of the tree are scored
and summed over all the nodes in each possible tree. The lowest-scoring tree sum provides
both an optimal tree and an optimal MSA given the scoring function. Because the method is
highly computationally intensive, an approximate method in which initial guesses for the
interior alignments are refined one node at a time. Both the full and the approximate
version are in practice calculated by dynamic programming. ^

MALIGN and POY

More recent phylogenetic tree/MSA methods use heuristics to isolate high-scoring, but not
necessarily optimal, trees. The MALIGN method uses a maximum-parsimony technique to
compute a multiple alignment by maximizing a cladogram score, and its companion POY
uses an iterative method that couples the optimization of the phylogenetic tree with
improvements in the corresponding MSA. However, the use of these methods in
constructing evolutionary hypotheses has been criticized as biased due to the deliberate
construction of trees reflecting minimal evolutionary events. Both programs are
available from the American Museum of Natural History

Computational phylogenetics 232

Maximum likelihood

The maximum likelihood method uses standard statistical techniques for inferring
probability distributions to assign probabilities to particular possible phylogenetic trees.
The method requires a substitution model to assess the probability of particular mutations;
roughly, a tree that requires more mutations at interior nodes to explain the observed
phylogeny will be assessed as having a lower probability. This is broadly similar to the
maximum-parsimony method, but maximum likelihood allows additional statistical flexibility
by permitting varying rates of evolution across both lineages and sites. In fact, the method
requires that evolution at different sites and along different lineages must be statistically
independent. Maximum likelihood is thus well suited to the analysis of distantly related
sequences, but because it formally requires search of all possible combinations of tree
topology and branch length, it is computationally expensive to perform on more than a few
sequences.

The "pruning" algorithm, a variant of dynamic programming, is often used to reduce the
search space by efficiently calculating the likelihood of subtrees. The method calculates
the likelihood for each site in a "linear" manner, starting at a node whose only descendants
are leaves (that is, the tips of the tree) and working backwards toward the "bottom" node in
nested sets. However, the trees produced by the method are only rooted if the substitution
model is irreversible, which is not generally true of biological systems. The search for the
maximum-likelihood tree also includes a branch length optimization component that is
difficult to improve upon algorithmically; general global optimization tools such as the
Newton-Raphson method are often used. Searching tree topologies defined by likelihood
has not been shown to be NP-complete, but remains extremely challenging because
branch-and-bound search is not yet effective for trees represented in this way.

Bayesian inference

Bayesian inference can be used to produce phylogenetic trees in a manner closely related
to the maximum likelihood methods. Bayesian methods assume a prior probability
distribution of the possible trees, which may simply be the probability of any one tree
among all the possible trees that could be generated from the data, or may be a more
sophisticated estimate derived from the assumption that divergence events such as
speciation occur as stochastic processes. The choice of prior distribution is a point of
contention among users of Bayesian-inference phylogenetics methods.

Implementations of Bayesian methods generally use Markov chain Monte Carlo sampling

algorithms, although the choice of move set varies; selections used in Bayesian

n 71
phylogenetics include circularly permuting leaf nodes of a proposed tree at each step L '

ri o]

and swapping descendant subtrees of a random internal node between two related trees.
The use of Bayesian methods in phylogenetics has been controversial, largely due to
incomplete specification of the choice of move set, acceptance criterion, and prior
distribution in published work. ]

Computational phylogenetics 233

Model selection

Molecular phylogenetics methods rely on a defined substitution model that encodes a
hypothesis about the relative rates of mutation at various sites along the gene or amino acid
sequences being studied. At their simplest, substitution models aim to correct for
differences in the rates of transitions and transversions in nucleotide sequences. The use of
substitution models is necessitated by the fact that the genetic distance between two
sequences increases linearly only for a short time after the two sequences diverge from
each other (alternatively, the distance is linear only shortly before coalescence). The longer
the amount of time after divergence, the more likely it becomes that two mutations occur at
the same nucleotide site. Simple genetic distance calculations will thus undercount the
number of mutation events that have occurred in evolutionary history. The extent of this
undercount increases with increasing time since divergence, which can lead to the
phenomenon of long branch attraction, or the misassignment of two distantly related but
convergently evolving sequences as closely related. The maximum parsimony method is
particularly susceptible to this problem due to its explicit search for a tree representing a
minimum number of distinct evolutionary events.

Types of models

All substitution models assign a set of weights to each possible change of state represented
in the sequence. The most common model types are implicitly reversible because they
assign the same weight to, for example, a G>C nucleotide mutation as to a C>G mutation.
The simplest possible model, the Jukes-Cantor model, assigns an equal probability to every
possible change of state for a given nucleotide base. The rate of change between any two
distinct nucleotides will be one-third of the overall substitution rate. More advanced
models distinguish between transitions and transversions. The most general possible
time-reversible model, called the GTR model, has contains six mutation rate parameters. An
even more generalized model known as the general 12-parameter model breaks
time-reversibility, at the cost of much additional complexity in calculating genetic distances
that are consistent among multiple lineages. One possible variation on this theme adjusts
the rates so that overall GC content - an important measure of DNA double helix stability -
varies over time.

Models may also allow for the variation of rates with positions in the input sequence. The
most obvious example of such variation follows from the arrangement of nucleotides in
protein-coding genes into three-base codons. If the location of the open reading frame
(ORF) is known, rates of mutation can be adjusted for position of a given site within a
codon, since it is known that wobble base pairing can allow for higher mutation rates in the
third nucleotide of a given codon without affecting the codon's meaning in the genetic
code. A less hypothesis-driven example that does not rely on ORF identification simply
assigns to each site a rate randomly drawn from a predetermined distribution, often the
gamma distribution or log-normal distribution. Finally, a more conservative estimate of
rate variations known as the covarion method allows autocorrelated variations in rates, so
that the mutation rate of a given site is correlated across sites and lineages.

Computational phylogenetics 234

Choosing the best model

The selection of an appropriate model is critical for the production of good phylogenetic
analyses, both because underparameterized or overly restrictive models may produce
aberrant behavior when their underlying assumptions are violated, and because overly
complex or overparameterized models are computationally expensive and the parameters
may be overfit. The most common method of model selection is the likelihood ratio test
(LRT), which produces a likelihood estimate that can be interpreted as a measure of
"goodness of fit" between the model and the input data. However, care must be taken in
using these results, since a more complex model with more parameters will always have a
higher likelihood than a simplified version of the same model, which can lead to the naive
selection of models that are overly complex. For this reason model selection computer
programs will choose the simplest model that is not significantly worse than more complex
substitution models. A significant disadvantage of the LRT is the necessity of making a
series of pairwise comparisons between models; it has been shown that the order in which
the models are compared has a major effect on the one that is eventually selected.

An alternative model selection method is the Akaike information criterion (AIC), formally an
estimate of the Kullback-Leibler divergence between the true model and the model being
tested. It can be interpreted as a likelihood estimate with a correction factor to penalize
overparameterized models. The AIC is calculated on an individual model rather than a
pair, so it is independent of the order in which models are assessed. A related alternative,
the Bayesian information criterion (BIC), has a similar basic interpretation but penalizes
complex models more heavily. '

See also

List of phylogenetics software

Cladistics

PHYLIP

Phylogenetic comparative methods

Phylogenetic tree

Phylogenetics

Systematics

Joe Felsenstein

External links

PHYLIP [23 , a freely distributed phylogenetic analysis package

PAUP , a similar analysis package available for purchase

MrBayes , a program for the Bayesian estimation of phylogeny (software wiki [ ] )

T271

BAli-Phy , a program for simultaneous Bayesian estimation of alignment and

phylogeny.

Treefinder , a graphical analysis environment for molecular phylogenetics

Modeltest , a program for selecting appropriate substitution models for nucleotide

sequences

CIPRES: Cyberinfrastructure for Phylogenetic Research [ ]

[Til

Phylogenetic inferring on the T-REX server
List of phylogeny programs
Phylogeny Algorithms Pseudocode

Computational phylogenetics 235

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Computational phylogenetics 236

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Newton's laws of motion Source: http://en.wikipedia.org/windex.php?oldid=296067593 Contributors: 21655, 5IIHoova, 963kickemall, @pple, A More
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Yurik, Yuyudevil, Zadeez, Zenzic, Zephyr9, Zginder, Zsinj, Zzyzxll, [][][][][][][][][]- 1862 anonymous edits

Analytical dynamics Source: http://en.wikipedia.org/windex.php?oldid=292074711 Contributors: Brews ohare, Djr32, Ideal gas equation, RHB100,
Rich Farmbrough, Sanpaz, 1 anonymous edits

Molecular dynamics Source: http://en.wikipedia.org/windex.php?oldid=295309203 Contributors: Agilemolecule, Alex.g, Amire80, Ammatsun,
Anthracene, Anxdo, Apjilly, Astavats, Ayucat, Bbullot, Bduke, BenFrantzDale, Bubba hotep, Chris the speller, Cortonin, Cwassman, DMacks, DRider,
Dacb, DeadEyeArrow, Demus Wiesbaden, Dicklyon, Dietmar.paschek, Dragonfly Sixtys even, Drswenson, Ebuchol, Ehdr, Gentgeen, Giftlite, Huckit,
Itamblyn, Itub, JWSchmidt, Jerome Charles Potts, Jorgenumata, Jugander, Kaihsu, Karol Langner, Katherine Folsom, Kennylam, Kevyn, Kjaergaard,
Knordlun, Laurentl979, Lexor, LiDaobing, Linas, Lomenoldur, Ludx, Maduixa, Marchuta, Marx Gomes, Mateusz Galuszka, Mattopia, Md Arshad Iqbal,
Mihoopes, Mr Marie Weaver, Msuzen, Nicolasbock, Oiramrasec, Opabinia regalis, Ossi, P99am, Paul.raymond.brenner, Pedrito, Pelister, PhCOOH,
Pksach, PrometheusX303, Raviwiki4, Rob Hooft, Rool812, Sandycx, Shura58, Smoe, Smremde, Stewartadcock, Sudiarta, TStein, Themfromspace,
Thorwald, Utcursch, Van helsing, Whanrott, Wikimcmd, Wittgenstein77, Wiz9999, Xavier andrade, Yrtgm, 200 anonymous edits

CHARMM Source: http://en.wikipedia.org/windex.php?oldid=296182826 Contributors: Betacommand, Btmiller, Closedmouth, DMacks, Dmb000006,
Dysprosia, Headbomb, ISGTW, Itub, Jagl23, Jedgold, Joerg Kurt Wegner, Johnpacklambert, Jorgenumata, Kaihsu, Karol Langner, LizGere, Mark Oakley,
Mndoci, P99am, PhCOOH, Rich Farmbrough, Shura58, Taw, ThomasK, Thorwald, Trevyn, Vicki Rosenzweig, Vincent kraeutler, 23 anonymous edits

Statistical mechanics Source: http://en.wikipedia.org/windex.php?oldid=294155089 Contributors: APH, Abtract, Aleksas, Alison, Ancheta Wis,
Andries, Anoko moonlight, Ap, Boardhead, Bogdangiusca, Brews ohare, Brianjd, Bryan Derksen, BryanD, Charles Matthews, Charvest, Chrisch,
Complexica, Conversion script, Cordell, DMTagatac, Dancter, Daniel5127, Davennmarr, David Woolley, Den fjattrade ankan, DiceDiceBaby, Djr32, Djus,

Computational phylogenetics 238

Doprendek, EdgarlSl, Edkarpov, Edsanville, Elwikipedista, Eman, Fephisto, Frokor, G716, Gail, GangofOne, Giftlite, Gurch, HappyCamper, Ht686rg90,
Isopropyl, IvanLanin, JabberWok, Jheald, John Palkovic, Jorgenumata, Karl-Henner, Karol Langner, Kzollman, Lantonov, LeadSongDog, Linas, Linuxlad,
Locke9k, Loupeter, Lyonspen, MK8, Mary blackwell, Met mht, Michael Hardy, Michael L. Kaufman, Miguel, Mikez, Mlys, Monedula, Moondarkx, Mpatel,
Mxn, Nitya Dharma, Nnh, P99am, PAR, Patrick, Peabeejay, Perelaar, Peterlin, Phudga, Phys, PhysPhD, Politepunk, Radagast83, RandomP, Rjwilmsi,
Ryanmcdaniel, SDC, Sadi Carnot, Samkung, Scorwin, Sheliak, SimpsonDG, Steve Omohundro, StewartMH, StradivariusTV, Template namespace
initialisation script, That Guy, From That Show!, The Anome, The Cunctator, The Original Wildbear, The.orpheus, Thingg, ThorinMuglindir, Tim Starling,
TravisAF, Truthnlove, Van helsing, Vql, Wavelength, Weiguxp, Wiki me, Xp54321, Yevgeny Kats, Yill577, 114 anonymous edits

Statistical field theory Source: http://en.wikipedia.org/windex. php?oldid=251854946 Contributors: Dolphin238, G716, Laurascudder, Maliz, Oleg
Alexandrov, R.e.b., Stewers, 16 anonymous edits

Computational chemistry Source: http://en.wikipedia.org/windex.php?oldid=294143278 Contributors: 194.200. 130.xxx, 41ex, 66.122.54.xxx, APH,
AcidFlask, Agilemolecule, Ahoerstemeier, Alexandrov, Altenmann, Andyras, Annabel, Arteum, Ashujo, BRG, Bduke, BenFrantzDale, CYD, Cdr Harris Fan
Club, Charles Matthews, Chmrjg, ConceptExp, Conversion script. Cyan, DV8 2XL, Edsanville, El C, Epbrl23, Feitclub, Fuzheado, Gentgeen, Ghutchis,
Giftlite, Giggy, Glloq, Grimlock, Gseryakov, Gurch, HRV, HappyCamper, Harold f, Hlwoodcock, Hugo-cs, Huttite, Iridium77, Isidore, Isilanes, Itub, JJL,
James 007, Jantony420, JerrySteal, Jitse Niesen, Jocelyne Heys-Gerard, JustMyself, Kaihsu, Kaiserkarll3, Karol Langner, Kku, Kmarkey, Knights who say
ni, Larry laptop, Lawrence O'Neil, Lexor, Lfh, LiDaobing, LuchoX, Marcoacostareyes, Marj Tiefert, Maurreen, Mayumashu, Mboverload, Michael Devore,
Moink, Mxn, NNemec, NuclearWinner, Od Mishehu, Okedem, Oleg Alexandrov, Oneboy, OrgasGirl, P.wormer, P99am, Paul August, PhCOOH, Poszwa,
ProteusCoop, Quanda, Ralf Schmelter, Rjwilmsi, Ronnotel, Roswell native, Rpetrenko, Ruud Koot, Sadi Carnot, Sam Hocevar, Samuel Grant, Sbo,
SeventyThree, Shyamal, Spike Wilbury, Stewartadcock, Stone, Swheele2, Themfromspace, TimBentley, Timwi, Tomturner, Tomtzigt, Van helsing, Vb,
Vina, Voorlandt, WhinerOl, ~K, 154 anonymous edits

Mathematical chemistry Source: http://en.wikipedia.org/windex.php?oldid=295232989 Contributors: Altenmann, Baz. 77. 243. 99. 32, DMacks, Giftlite,
Hamleteer, Itub, Linas, Maxal, Mpatel, Niksab, Remuel, Tim32, 10 anonymous edits

Monte Carlo method Source: http://en.wikipedia.org/windex.php?oldid=295834903 Contributors: *drew, ABCD, Aardvark92, Adfredl23, Aferistas,
Agilemolecule, Akanksh, Alanbly, Albmont, AlexBIOSS, AlexandreCam, AlfredR, Alliance09, Altenmann, Andrea Parri, Andreas Kaufmann, Angelbo, Aniu,
Apanag, Aspuru, Atlant, Avalcarce, Aznrocket, BAxelrod, BConleyEEPE, Banano03, Banus, Bduke, BenFrantzDale, BenTrotsky, Bender235, Bensaccount,
BillGosset, BkelL Blotwell, Bmaddy, Bobol92, Boffob, Boredzo, Broquaint, Btyner, CRGreathouse, Caiaffa, Charles Matthews, ChicagoActuary, Cibergili,
Cm the p, Colonies Chris, Coneslayer, Cretog8, Criter, Cybercobra, Cythonl, DMG413, Damistmu, Ddcampayo, Ddxc, Digemedi, Ds53, Duck ears,
Duncharris, Dylanwhs, ERosa, EldKatt, Elpincha, Elwikipedista, Eudaemonic3, Ezrakilty, Fastfission, Fintor, Flammifer, Frozen fish, Furrykef, G716,
Giftlite, Gilliam, Goudzovski, GraemeL, GrayCalhoun, Greenyoda, Grestrepo, Gtrmp, Gokhan, Hanksname, Hawaiian717, Hokanomono, Hul2,
Hubbardaie, ILike Things, IanOsgood, Inrad, Itub, Jackal irl, Janpedia, JavaManAz, Jeffq, Jitse Niesen, Joey0084, JohnOwens, Jorgenumata, Jsarratt,
Jugander, Jerome, K.lee, KSmrq, KaHa242, Karol Langner, Kenmckinley, Kimys, Knordlun, Kroese, Kummi, Kuru, Lambyte, LeoTrottier, Levin, Lexor,
LoveMonkey, Malatesta, Malel979, ManchotPi, Marcofalcioni, Martinp, Masatran, Mathcount, MaxHD, Maxentrope, Maylene, Melcombe, Michael
Hardy, Mikael V, Misha Stepanov, Mnath, Moink, Mtford, Nagasaka, Nanshu, Narayanese, Nelson50, Nosophorus, Nsaa, Nuno Tavares, Nvartaniucsd,
Ohnoitsjamie, Oli Filth, Oneboy, Orderud, OrgasGirl, P99am, Paul August, PaulxSA, Pbroksl3, Pcb21, Pete.Hurd, PeterBoun, Pgreenfinch, Philopp,
Pibwl, Pinguin.tk, PlantTrees, Pne, Popsracer, Poupoune5, Qadro, Quantumelfmage, Quentar, Qxz, RWillwerth, Ramin Nakisa, Redgolpe, Renesis, Richie
Rocks, Rinconsoleao, Rjmccall, Ronnotel, Rs2, SKellyl313, Sam Korn, Samratvishaljain, Sergio.ballestrero, Shreevatsa, Snoyes, Somewherepurple,
Spellmaster, Splash6, SpuriousQ, Stefanez, Stefanomione, StewartMH, Stimpy, Storm Rider, Superninja, Tarantola, Taxman, Tayste, Tesil700,
TheronllO, Thirteenity, Tiger Khan, Tim Starling, Tom harrison, Tooksteps, Trebor, Twooars, Urdutext, Vipuser, VoseSoftware, Wile E. Heresiarch,
Yoderj, Zarniwoot, Zoicon5, Zr40, Zuidervled, 308 anonymous edits

Quantum Monte Carlo Source: http://en.wikipedia.org/windex.php?oldid=295037474 Contributors: Acipsen, Amyoungil, Bci2, Conscious, Henry
Delforn, Isilanes, Jheriko, Karol Langner, Lucaskw, Mdt26a, Melcombe, Michael Hardy, NNemec, Pablomme, Paulcardan, Rbonvall, Rich Farmbrough,
Rjwilmsi, Sagaciousuk, Supersion77, TestPilot, Trigger hippie77, UkPaolo, Veinor, Vgy7ujm, Vyznev Xnebara, WilliamDParker, WirawanO, 38 anonymous
edits

Dynamics of Markovian particles Source: http://en.wikipedia.org/windex.php?oldid=275949632 Contributors: Bergner, Czolgolz, ERobson,
Fabrictramp, Icairns, JPG-GR, Malcolma, Mbell, Oleg Alexandrov, ShakespeareFanOO, 14 anonymous edits

Metabolic network Source: http://en.wikipedia.org/windex.php?oldid=231870375 Contributors: Blastwizard, Ceyockey, Oleginger, PDH,
TheParanoidOne, TimVickers, Zephyris, 2 anonymous edits

Topological dynamics Source: http://en.wikipedia.org/windex.php?oldid=285184911 Contributors: Arcfrk, Charvest, Michael Hardy, SiamakT

Protein folding Source: http://en.wikipedia.org/windex.php?oldid=295343721 Contributors: 168..., 5beta5, Adriferr, Agilemolecule, Akane700,
Andraaide, Arcadian, Banus, Barticus88, Bci2, Bendzh, Bfinn, Bioinfol77, Biophys, Biophysik, Blainster, Blooooo, Brianga, Bryan Derksen, Cacycle,
CalveroJP, Cathalgarvey, Cburnett, ChicXulub, Clicketyclack, Computor, Cyberman, Czhangrice, D. Recorder, DannyWilde, Davepntr, DennisDaniels,
Dhatz, Donarreiskoffer, Dwmyers, ESkog, Eequor, Erencexor, Erwinser, Fawzin, Fuzheado, Gcrossan, Gowantervo, Grimlock, Harley peters, Herd of
Swine, Hooplehead, Intangir, Ixfd64, JJ TKOB, Jacobsman, Jammedshut, JeramieHicks, Katherine Folsom, Kevyn, Kierano, Kjaergaard, Konstantin,
Kostmo, Leptictidium, Lexor, Lfh, LiDaobing, Lir, Lostart, Lucaaah, M stone, MacintoshlOOOO, Madeleine Price Ball, Magnus Manske, Malcolm Farmer,
Mark Renier, Michael Hardy, Miguel Andrade, Minghong, MockAE, Movado73, Movalley, Myscrnnm, Netesq, Opabinia regalis, Otvaltak, P99am, Piotrus,
Ptrl23, RDBrown, Rebroad, Richyfp, Rjwilmsi, RoyBoy, RunninRiot, Samrat Mukhopadhyay, Sharkman, Shmedia, SirHaddock, Smelialichu,
Snowmanradio, Splette, SpuriousQ, Stepa, Sunnyl7152, Taw, Terrace4, TestPilot, The Anome, The Great Cook, Tijmz, TimVickers, Tomixdf, Tommstein,
Toytoy, Trenchcoatjedi, Trusilver, V8rik, Waerloeg, WillowW, WorldDownlnFire, Xnuala, Xy7, Yves-henri, Zoicon5, TNI"), 147 anonymous edits

Protein-protein interaction Source: http://en.wikipedia.org/windex.php?oldid=293638290 Contributors: 56869kltaylor, 7bdl, A wandering 1,
Alboyle, Apfelsine, Ashcroft, Bci2, Biophys, Clicketyclack, Cpichardo, D-rew, DarkSaber2k, Delldot, Djstates, Dsome, FreeKill, Giftlite, GracelinTina,
Hendrik Fuft, Hotheartdog, Jeandre du Toit, Jkbioinfo, Jkwaran, Jn3vl6, Jongbhak, Keesiewonder, Kkmurray, Kuheli, Kyawtun, Lafw, Lemchesvej,
Lenticel, Longhair, Meb025, Michael Hardy, MichaelMcGuffin, Miguel Andrade, NickelShoe, Ninjagecko, Nnh, Rajah, Reb42, Riana, Ronz, Seans Potato
Business, Snowolf, TheParanoidOne, Thorwald, Uthbrian, Victor D, Wenzelr, Whosasking, Wintrag, 67 anonymous edits

DNA Dynamics Source: http://en.wikipedia.org/windex.php?oldid=296104632 Contributors: Auntof6, Bci2, CanderOOOO, Chris the speller,
CommonsDelinker, Ironholds, Potatoswatter

DNA nano technology Source: http://en.wikipedia.org/windex.php?oldid=294763628 Contributors: 0x38I9J*, Alnokta, Amaling, Anthonydelaware,
Antony-22, Cyfal, Epbrl23, Giftlite, Gioto, Pwkr, ShawnDouglas, Thorwald, Tolosthemagician, ZayZayEM, 30 anonymous edits

Molecular self-assembly Source: http://en.wikipedia.org/windex.php?oldid=295612777 Contributors: Antony-22, Dirac66, LithoGuy, M stone,
Materialscientist, Maurog, Mdd, Nanotrix, Netmonger, Northfox, Rudick.JG, Satish.murthy, TestPilot, 21 anonymous edits

Cell signaling Source: http://en.wikipedia.org/windex.php?oldid=294194237 Contributors: A-Day, Amenzix, Annekcm, Apfelsine, Arcadian, B9
hummingbird hovering, Biochemza, Clicketyclack, Computerjoe, Dlohcierekim, DrTLesterThomas, Drphilharmonic, Edgarl81, Fannaba, Fritzpoll,
H overfly smiles, JWSchmidt, K.murphy, Lenticel, Letranova, Lkathmann, Lunska, Mandarax, Mdd, Mikael Haggstrom, Nanobri, Nemenman, Neutrality,
Nihiltres, OldakQuill, PaddyM, Physicistjedi, Popo le Chien, Pozzie, Radagast83, Rjwilmsi, Sardaukar Blackfang, Seans Potato Business, Shell Kinney,
Squidonius, Tabletop, Tameeria, Tikiwont, Vary, Wisdom89, Wolfrock, Woohookitty, Ynaztiw, 49 anonymous edits

Molecular evolution Source: http://en.wikipedia.org/windex.php?oldid=294465595 Contributors: lOoutoflOdie, 168..., A.bit, AdamRetchless, Aranae,
Aunt Entropy, AxelBoldt, Ben Tillman, Borgx, Bornhj, Debresser, Duncharris, Emw2012, Etxrge, Eugene van der Pijll, Ewen, GSlicer, Gaius Cornelius,
GeoMor, Kosigrim, Lexor, Lindosland, M stone, MER-C, Marooned Morlock, Mewl 139, Neutrality, Nonsuch, Northfox, Notreallydavid, OnBeyondZebrax,
Owenman, PDH, PhDP, Ragesoss, Rigadoun, Ryulong, Sadi Carnot, Samsara, Seglea, Shyamal, Steinsky, Stirling Newberry, StormBlade, Swpb, Template
namespace initialisation script, That Guy, From That Show!, The Anome, Theuser, Thue, Timwi, Vsmith, Wavesmikey, Whatiguana, 52 anonymous edits

Computational phylogenetics 239

Molecular phylogenetics Source: http://en.wikipedia.org/windex.php?oldid=295503179 Contributors: 168..., Aranae, Brya, Carlosp420,
Dysmorodrepanis, Edjohnston, Eugene van der Pijll, Florentino floro, Igodard, JForget, Jojan, Joseph Solis in Australia, Kingdon, Lexor,
Mlsslontomars2k4, Mariol952, Marj Tiefert, Onco p53, Otherlleft, PierreAbbat, Radagast83, Ragesoss, RoRo en wiki, Samsara, Shyamal, Sinneed,
Stemonitis, StephenWeber, Styrofoaml994, 20 anonymous edits

Computational phylogenetics Source: http://en.wikipedia.org/windex.php?oldid=281615251 Contributors: Aranae, Dysmorodrepanis, Fred Hsu,
Hongooi, J. Spencer, JohnnyHom, Lambiam, Leonard G., MrDolomite, Noleander, Opabinia regalis, Ramesan, Thorwald, Whatiguana, Wild8oar,
Wzhao553, 9 anonymous edits

Computational phylogenetics 240

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Copyright (C) 2000,2001,2002 Free Software Foundation, Inc.
51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

0. PREAMBLE

The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone
the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License
preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.
This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the
GNU General Public License, which is a copyleft license designed for free software.

We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should
come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any
textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose
is instruction or reference.

1. APPLICABILITY AND DEFINITIONS

This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under

the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated

herein. The "Document", below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as "you". You accept the

license if you copy, modify or distribute the work in a way reguiring permission under copyright law.

A "Modified Version" of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or

translated into another language.

A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or

authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject.

(Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter

of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

The "Invariant Sections" are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the

Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant.

The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

The "Cover Texts" are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document

is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

A "Transparent" copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public,

that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for

drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats

suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to

thwart or discourage subseguent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of

text. A copy that is not "Transparent" is called "Opaque".

Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using

a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image

formats include PNG, XCF and JPG. Opague formats include proprietary formats that can be read and edited only by proprietary word processors, SGML

or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some

word processors for output purposes only.

The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License

requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent

appearance of the work's title, preceding the beginning of the body of the text.

A section "Entitled XYZ" means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that

translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as "Acknowledgements", "Dedications",

"Endorsements", or "History".) To "Preserve the Title" of such a section when you modify the Document means that it remains a section "Entitled XYZ"

according to this definition.

The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers

are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty

Disclaimers may have is void and has no effect on the meaning of this License.

2. VERBATIM COPYING

You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices,
and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to
those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute.
However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in
section 3.
You may also lend copies, under the same conditions stated above, and you may publicly display copies.

3. COPYING IN QUANTITY

If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's
license notice reguires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the
front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front
cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying
with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in
other respects.

If the reguired texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover,
and continue the rest onto adjacent pages.

If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy
along with each Opague copy, or state in or with each Opague copy a computer-network location from which the general network-using public has
access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter
option, you must take reasonably prudent steps, when you begin distribution of Opague copies in guantity, to ensure that this Transparent copy will
remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or
retailers) of that edition to the public.

It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a
chance to provide you with an updated version of the Document.

4. MODIFICATIONS

You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified
Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the
Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

1 . Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there
were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version
gives permission.

2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together
with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this
requirement.

3. State on the Title page the name of the publisher of the Modified Version, as the publisher.

4. Preserve all the copyright notices of the Document.

5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.

6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this
License, in the form shown in the Addendum below.

7. Preserve in that license notice the full lists of Invariant Sections and reguired Cover Texts given in the Document's license notice.

License 245

8. Include an unaltered copy of this License.

9. Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the
Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and
publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.

10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network
locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network
location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives
permission.

11. For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and
tone of each of the contributor acknowledgements and/or dedications given therein.

12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered
part of the section titles.

13. Delete any section Entitled "Endorsements". Such a section may not be included in the Modified Version.

14. Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section.

15. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the

Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the

Modified Version's license notice. These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties-for example,

statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover

Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by)

any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity

you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the

old one.

The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply

endorsement of any Modified Version.

5. COMBINING DOCUMENTS

You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions,

provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant

Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are

multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in

parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section

titles in the list of Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise

combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements."

6. COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this
License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim
copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into
the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

7. AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution
medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond
what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which
are not themselves derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire
aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers
if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

8. TRANSLATION

Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant
Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in
addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document,
and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and
disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will
prevail.

If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will
typically require changing the actual title.

9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except as expressly provided for under this License. Any other attempt to copy, modify,
sublicense or distribute the Document is void, and will automatically terminate your rights under this License. However, parties who have received
copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.

10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be
similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.
Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or
any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has
been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any
version ever published (not as a draft) by the Free Software Foundation.

How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices
just after the title page:

Permission is granted to copy, distribute and/or modify this document

under the terms of the GNU Free Documentation License, Version 1.2

or any later version published by the Free Software Foundation;

with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

A copy of the license is included in the section entitled "GNU

Free Documentation License".
If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with. ..Texts." line with this:

with the Invariant Sections being LIST THEIR TITLES, with the

Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.
If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.
If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software
license, such as the GNU General Public License, to permit their use in free software.

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